Ophthalmic data measuring apparatus, ophthalmic data measurement program and eye characteristic measuring apparatus

ABSTRACT

It is possible to estimate optical characteristic according to a pupil diameter in daily life of an examinee, correction data near to the optimal prescription value, eyesight, and sensitivity. A calculation section receives measurement data indicating refractive power distribution of an eye to be examined and pupil data on the eye and calculates lower order and higher order aberrations according to the measurement data and the pupil data (S 101  to  105 ). For example, a pupil edge is detected from the anterior ocular segment image and a pupil diameter is calculated. By using this pupil diameter, lower order and higher order aberrations are calculated. According to the lower order and higher order aberrations obtained, the calculation section performs simulation of a retina image by using high contrast or low contrast target and estimates the eyesight by comparing the result to a template and/or obtains sensitivity (S 107 ). Alternatively, according to the lower order and the higher order aberrations obtained, the calculation section calculates an evaluation parameter indicating the quality of visibility by the eye to be examined such as the Strehl ratio, the phase shift (PTF), and the visibility by comparison of the retina image simulation with the template. According to the evaluation parameter calculated, the calculation section changes the lower order aberration amount so as to calculate appropriate correction data for the eye to be examined (S 107 ). The calculation section outputs data such as the eyesight, sensitivity, correction data, and the simulation result to a memory or a display section (S 109 ).

TECHNICAL FIELD

The present invention relates to an ophthalmic data measuring apparatusfor measuring appropriate correction data and/or estimating visualacuity in daily life, an ophthalmic data measurement program and an eyecharacteristic measuring apparatus.

BACKGROUND ART

Conventionally, as a technique for measuring ocular correction data,measurement of S (Sphere), C (Cylinder) and A (axis) by a refractometerhas been carried out. Besides, recently, an eye characteristic measuringapparatus capable of measuring higher order aberrations has also beendeveloped, and not only S, C and A on a line like, for example, a ringof φ3 mm as in a refractometer, but also S, C and A on a plane when apupil diameter is made various sizes can be calculated from lower orderaberrations. By the eye characteristic measuring apparatus like this,especially after a refraction correcting surgical operation or in an eyedisease, values closer to prescription values of eyeglasses or contactlenses than the refractometer can be calculated (for example, seeJP-A-2002-204785, JP-A-2002-209854, JP-A-2002-306416, JP-A-2002-306417,etc.).

Besides, as an apparatus for displaying the visibility of a subjectiveeye at the time of correction or by the eye, an apparatus by the presentapplicant is disclosed (for example, see JP-A-2001-120504,JP-A-7-100107). In these apparatuses, for example, the visibility of apredetermined index is displayed on display means based on the measuredoptical characteristic of the eye to be examined (eye to be measured).

DISCLOSURE OF THE INVENTION

However, in the objective calculation results of the conventional eyecharacteristic measuring apparatus and prescription values ofeyeglasses, contacts, or the like, there is a case where a differencefrom an appropriate value occurs, and there has been a case where theyare insufficient as evaluation of S, C and A. Besides, conventionally,since a measurement is made using a fixed value as the pupil diameter ofan eye to be examined, there has been a case where an appropriateprescription value corresponding to the pupil diameter of the eye to beexamined can not be obtained.

Besides, in the conventional measurement, although the visibility of anindex or the like is displayed, the visual acuity of the subjective eyeis not estimated. Further, the prediction of the visibility is often thevisibility under a generally used visual acuity measurement condition,and the visibility and the visual acuity under an environment of the eyeto be examined, for example, in daily life, have not been obtained.

Besides, conventionally, when PSF or MTF on the retina is simplyevaluated, there has been a case where it is very difficult to obtain anappropriate evaluation, that is, a value close to a subjective test.

In view of the above, the invention has an object to calculate anoptical characteristic corresponding to a pupil diameter of an eye to beexamined and correction data close to an optimum prescription value andto perform more accurate measurement.

Besides, according to an object of the invention, in the measurementresults of an eye characteristic measuring apparatus which can measurehigher order aberrations, in the case where a higher order aberration isincluded, a lower order aberration corresponding to the time ofobjective complete correction is not made compensation correction data,optical performance is evaluated with, for example, a Strehl ratio or aphase shift, a lower order aberration amount by which the Strehl ratiobecomes large and/or the phase shift becomes small is calculated, andcompensation correction data of S, C, A and the like at that time isobtained, so that correction data close to the optimum prescriptionvalue of eyeglasses/contacts is obtained.

Further, an object is to obtain correction data close to a subjectivevalue by performing simulation of visibility of an index for eyeexamination to obtain an appropriate correction element.

The invention has an object to estimate visual acuity of an eye to beexamined in luminance corresponding to an environment of a subjectiveeye in daily life (for example, in the daytime or in a room). Besides,the invention has an object to estimate visual acuity with respect to anindex of high contrast and/or low contrast in view of a pupil diameterof an eye to be examined in daily life. The invention has an object topredict contrast sensitivity in view of a pupil diameter. Besides, theinvention has also an object according to which a pupil diameter inluminance corresponding to an environment of a subjective eye is used,correction data close to an optimum prescription value under theenvironment is obtained, and the visual acuity under the environment ofthe subjective eye at the time of correction by the obtained correctiondata is estimated. Besides, the simulation of an index, such as aLandolt's ring, on the retina in view of the size of a pupil areacalculated in the middle of the process is also singly effective.

According to the first solving means of this invention, there isprovided, an ophthalmic data measuring apparatus comprising:

a first light source part to emit a light flux of a first wavelength;

a first illuminating optical system for performing illumination tocondense the light flux from the first light source part on a vicinityof a retina of an eye to be examined;

a first light receiving optical system for receiving a part of the lightflux reflected by and returning from the retina of the eye to beexamined through a first conversion member to convert it into at leastsubstantially 17 beams;

a first light receiving part for receiving the received light flux ofthe first light receiving optical system; and

a calculation section to perform Zernike analysis based on aninclination angle of the light flux obtained by the first lightreceiving part, to obtain an optical characteristic of the eye to beexamined, and (1) to estimate one of or two or more of a visual acuity,the optical characteristic and a sensitivity of the eye to be examinedunder an observation condition corresponding to an environment of theeye to be examined, or (2) to calculate appropriate correction datasuitable for the eye to be examined,

wherein the calculation section comprises:

first means for obtaining measurement data indicating a refractive powerdistribution of the eye to be examined and pupil data including a valueof a pupil diameter of the eye to be examined or a pupil diameter imageand for obtaining lower order aberrations and higher order aberrationsbased on an observation condition parameter including the measurementdata and the pupil data;

second means for calculating an evaluation parameter indicating qualityof visibility by the eye to be examined based on the observationcondition parameter and/or the obtained lower order aberrations and thehigher order aberrations; and

third means for, in accordance with the calculated evaluation parameter,(1) estimating one of or two or more of the visual acuity, the opticalcharacteristic and the sensitivity, of the eye to be examined under theobservation condition corresponding to the environment of a subjectiveeye or (2) calculating the appropriate correction data suitable for theeye to be examined by changing the lower order aberration.

According to the second solving means of this invention, there isprovided, an ophthalmic data measurement program for causing a computerto execute:

a first step at which a calculation section obtains measurement dataindicating a refractive power distribution of an eye to be examined andpupil data including a value of a pupil diameter of the eye to beexamined or a pupil diameter image, and obtains lower order aberrationsand higher order aberrations based on an observation condition parameterincluding the measurement data and the pupil data;

a second step at which the calculation section calculates an evaluationparameter indicating quality of visibility by the eye to be examinedbased on the observation condition parameter and/or the obtain lowerorder aberrations and the higher order aberrations; and

a third step at which in accordance with the calculated evaluationparameter, the calculation section estimates one of or two or more of avisual acuity, an optical characteristic and a sensitivity of the eye tobe examined under an observation condition corresponding to anenvironment of a subjective eye, or calculates appropriate correctiondata suitable for the eye to be examined by changing the lower orderaberration.

According to the third solving means of this invention, there isprovided, an ophthalmic data measurement program for causing a computerto execute:

a first step at which a calculation section receives measurement dataindicating a refractive power distribution of an eye to be examined, andobtains lower order aberrations and higher order aberrations based onthe measurement data;

a second step at which the calculation section calculates an evaluationparameter indicating quality of visibility by the eye to be examinedbased on the obtained lower order aberrations and the higher orderaberrations; and

a third step at which the calculation section calculates appropriatecorrection data suitable for the eye to be examined by changing thelower order aberration in accordance with the calculated evaluationparameter.

According to the fourth solving means of this invention, there isprovided, an eye characteristic measuring apparatus comprising:

a first light source part to emit a light flux of a first wavelength;

a first illuminating optical system for performing illumination tocondense the light flux from the first light source part on a vicinityof a retina of an eye to be examined;

a first light receiving optical system for receiving a part of the lightflux reflected by and returning from the retina of the eye to beexamined through a first conversion member to convert it into at leastsubstantially 17 beams;

a first light receiving part for receiving the received light flux ofthe first light receiving optical system; and

a calculation section for receiving pupil data including a pupil imageof the eye to be examined in a measurement environment, calculating apupil diameter under the measurement environment based on the receivedpupil data, and obtaining an optical characteristic of the eye to beexamined based on the calculated pupil diameter and an output signalfrom the first light receiving part.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a structural view of an optical system 100 of an eye opticalcharacteristic measuring apparatus.

FIG. 2 is a structural view of an electric system 200 of the eye opticalcharacteristic measuring apparatus.

FIG. 3 is an explanatory view of a Landolt's ring.

FIG. 4 is flowchart of ophthalmic data measurement.

FIG. 5 is a sub-flowchart concerning calculation of a pupil diameter andmeasurement of eye optical system data.

FIG. 6 is an explanatory view of pupil diameter calculation.

FIG. 7 is a first flowchart of simulation of visual acuity.

FIG. 8 is a flowchart of simulation of a retinal image.

FIG. 9 is an explanatory view of template matching.

FIG. 10 is a flowchart of Landolt's ring template matching.

FIG. 11 is a second flowchart (1) of simulation of visual acuity.

FIG. 12 is a second flowchart (2) of simulation of visual acuity.

FIG. 13 is a third flowchart of simulation of visual acuity.

FIG. 14 is a fourth flowchart of simulation of visual acuity.

FIG. 15 is an explanatory view of contrast sensitivity.

FIG. 16 shows a display example of visual acuity estimation by templatematching.

FIG. 17 shows a display example concerning comparison betweenpre-compensation and post-compensation.

FIG. 18 is an explanatory view of an example of prescription data foreyeglasses/contacts.

FIG. 19 is an explanatory view of an example of data for refractivesurgery.

FIG. 20 is an explanatory view of an example of prescription data foreyeglasses/contacts when an environmental condition is changed.

FIG. 21 is an explanatory view of an example of pupil data when anenvironmental condition is changed.

FIG. 22 is a comparison view of prescription data foreyeglasses/contacts with respect to measurement with a constant pupildiameter.

FIG. 23 is a flowchart of correction image simulation.

FIG. 24 is a flowchart concerning a first example of best imagecondition calculation.

FIG. 25 is a flowchart concerning a second example of best imagecondition calculation.

FIG. 26 is a view showing a display example of best image display-Strehlratio optimization.

FIG. 27 is a view showing a display example of best image display-PTFoptimization.

FIG. 28 is a view showing a display example concerning comparisonbetween pre-compensation and post-compensation.

FIG. 29 is an explanatory view of an example of prescription data foreyeglasses/contacts.

FIG. 30 is an explanatory view of an example of data for refractivesurgery.

FIG. 31 is an explanatory view of an example of prescription data foreyeglasses/contacts when an environmental condition is changed.

FIG. 32 is a comparison view of prescription data foreyeglasses/contacts with respect to measurement with a constant pupildiameter.

BEST MODE FOR CARRYING OUT THE INVENTION

FIG. 1 is a structural view of an optical system 100 of an eye opticalcharacteristic measuring apparatus (an ophthalmic data measuringapparatus).

The optical system 100 of the eye optical characteristic measuringapparatus is an apparatus for measuring an optical characteristic of aneye 60 to be measured as an object, and includes a first illuminatingoptical system 10, a first light receiving optical system 20, a secondlight receiving optical system 30, a common optical system 40, anadjusting optical system 50, a second illuminating optical system 70,and a second light sending optical system 80. Incidentally, with respectto the eye 60 to be measured, a retina 61 and a cornea 62 are shown inthe drawing.

The first illuminating optical system 10 includes, for example, a firstlight source part 11 for emitting a light flux of a first wavelength,and a condensing lens 12, and is for illuminating a minute area on theretina (retina) 61 of the eye 60 to be measured with the light flux fromthe first light source part 11 so that its illumination condition can besuitably set. Incidentally, here, as an example, the first wavelength ofthe illuminating light flux emitted from the first light source part 11is a wavelength (for example, 780 nm) of an infrared range.

Besides, it is desirable that the first light source part 11 has a highspatial coherence and a low temporal coherence. Here, the first lightsource part 11 is, for example, a super luminescence diode (SLD), and apoint light source having high luminescence can be obtained.Incidentally, the first light source part 11 is not limited to the SLD,and for example, a laser having a high spatial coherence and a hightemporal coherence can also be used by inserting a rotation diffusedplate or declination prism (D prism) or the like to suitably lower thetemporal coherence. Further, an LED having a low spatial coherence and alow temporal coherence can also be used, if light quantity issufficient, by inserting, for example, a pinhole or the like at aposition of a light source in an optical path.

The first light receiving optical system 20 includes, for example, acollimator lens 21, a Hartmann plate 22 as a conversion member forconverting a part of a light flux (first light flux) reflected andreturned from the retina 61 of the eye 60 to be measured into at least17 beams, and a first light receiving part 23 for receiving the pluralbeams converted by the Hartmann plate 22, and is for guiding the firstlight flux to the first light receiving part 23. Besides, here, a CCDwith little readout noise is adopted for the first light receiving part23, and as the CCD, a suitable type of CCD, for example, a general lownoise type of CCD, a cooling CCD of 1000*1000 elements for measurement,or the like is applicable.

The second illuminating optical system 70 includes a second light source72 and a Placido's disk 71. Incidentally, the second light source 72 canbe omitted. The Placido's disk (PLACIDO'S DISK) 71 is for projecting anindex of a pattern composed of plural co-axial rings. Incidentally, theindex of the pattern composed of the plural co-axial rings is an exampleof an index of a specified pattern, and a different suitable pattern canbe used. Then, after an alignment adjustment described later iscompleted, the index of the pattern composed of the plural co-axialrings can be projected.

The second light sending optical system 80 is for mainly performing, forexample, the alignment adjustment described later, and measurement andadjustment of a coordinate origin and a coordinate axis, and includes asecond light source part 31, a condensing lens 32, and a beam splitter33.

The second light receiving optical system 30 includes a condensing lens34 and a second light receiving part 35. The second light receivingoptical system 30 guides a light flux (second light flux), which isoriginated from the pattern of the Placido's disk 71 illuminated fromthe second illuminating optical system 70 and is reflected and returnedfrom the anterior eye part or the cornea 62 of the eye 60 to bemeasured, to the second light receiving part 35. Besides, it can alsoguide a light flux, which is emitted from the second light source part31 and is reflected and returned from the cornea 62 of the eye 60 to bemeasured, to the second light receiving part 35. Incidentally, as thesecond wavelength of the light flux emitted from the second light sourcepart 31, for example, a wavelength different from the first wavelength(here, 780 nm) and longer (for example, 940 nm) than that can beselected.

The common optical system 40 is disposed on an optical axis of the lightflux emitted from the first illuminating optical system 10, can beincluded in the first and the second illuminating optical systems 10 and70, the first and the second light receiving optical systems 20 and 30,the second light sending optical system 80 and the like in common, andincludes, for example, an afocal lens 42, beam splitters 43 and 45, anda condensing lens 44. The beam splitter 43 is formed of such a mirror(for example, a dichroic mirror) that the wavelength of the second lightsource part 31 is sent (reflected) to the eye 60 to be measured, and thesecond light flux reflected and returned from the retina 61 of the eye60 to be measured is reflected, and on the other hand, the wavelength ofthe first light source part 11 is transmitted. The beam splitter 45 isformed of such a mirror (for example, a polarization beam splitter) thatthe light flux of the first light source part 11 is sent (reflected) tothe eye 60 to be measured, and the first light flux reflected andreturned from the retina 61 of the eye 60 to be measured is transmitted.By the beam splitters 43 and 45, the first and the second light fluxesdo not mutually enter the other optical systems to generate noise.

The adjusting optical system 50 is for mainly performing, for example, aworking distance adjustment described later, includes a third lightsource part 51, a fourth light source part 55, condensing lenses 52 and53, and a third light receiving part 54, and is for mainly performingthe working distance adjustment.

A third illuminating optical system 90 includes an optical path forprojection of an index for causing, for example, fixation of the eye 60to be measured or fogging, and includes a fifth light source part (forexample, a lamp) 91, a fixation target 92 and a relay lens 93. Thefixation target 92 can be irradiated to the retina 61 by the light fluxfrom the fifth light source part 91, and the eye 60 to be measured ismade to observe its image. The fixation target 92 and the retina 61 areput in a conjugated relation by the third illuminating optical system90. Besides, the fifth light source part 91 is also a light source(anterior ocular segment illuminating part) to illuminate the anteriorocular segment of the eye 60 to be measured under different luminanceconditions. The light amount of the fifth light source part 91 isadjusted, so that the illumination state of the eye 60 to be measured ischanged and the size of the pupil can be changed. Incidentally, as theanterior ocular segment illuminating part, in addition to the fifthlight source part 91, an appropriate light source such as the secondlight source 72 may be used.

Next, the alignment adjustment will be described. The alignmentadjustment is mainly carried out by the second light receiving opticalsystem 30 and the second light sending optical system 80.

First, the light flux from the second light source part 31 illuminatesthe eye 60 to be measured as the object with the substantially parallellight flux through the condensing lens 32, the beam splitters 33 and 43,and the afocal lens 42. The reflected light flux reflected by the cornea62 of the eye 60 to be measured is emitted as a divergent light fluxsuch as is emitted from a point at the half of the radius of curvatureof the cornea 62. The divergence light flux is received as a spot imageby the second light receiving part 35 through the afocal lens 42, thebeam splitters 43 and 33, and the condensing lens 34.

Here, in the case where the spot image on the second light receivingpart 35 is outside the optical axis, the main body of the eye opticalcharacteristic measuring apparatus is moved and adjusted vertically andhorizontally, and the spot image is made to coincide with the opticalaxis. As stated above, when the spot image coincides with the opticalaxis, the alignment adjustment is completed. Incidentally, with respectto the alignment adjustment, the cornea 62 of the eye 60 to be measuredis illuminated by the third light source part 51, and an image of theeye 60 to be measured obtained by this illumination is formed on thesecond light receiving part 35, and accordingly, this image may be usedto make the pupil center coincide with the optical axis.

Next, the working distance adjustment will be described. The workingdistance adjustment is mainly carried out by the adjusting opticalsystem 50.

First, the working distance adjustment is carried out by, for example,irradiating the eye 60 to be measured with a parallel light flux emittedfrom the fourth light source part 55 and close to the optical axis, andby receiving the light reflected from the eye 60 to be measured throughthe condensing lenses 52 and 53 by the third light receiving part 54.Besides, in the case where the eye 60 to be measured is in a suitableworking distance, a spot image from the fourth light source part 55 isformed on the optical axis of the third light receiving part 54. On theother hand, in the case where the eye 60 to be measured goes out of thesuitable working distance, the spot image from the fourth light sourcepart 55 is formed above or below the optical axis of the third lightreceiving part 54. Incidentally, since the third light receiving part 54has only to be capable of detecting a change of a light flux position onthe plane containing the fourth light source part 55, the optical axisand the third light receiving part 54, for example, a one-dimensionalCCD arranged on this plane, a position sensing device (PSD) or the likeis applicable.

Next, a positional relation between the first illuminating opticalsystem 10 and the first light receiving optical system 20 will bedescribed.

The beam splitter 45 is inserted in the first light receiving opticalsystem 20, and by this beam splitter 45, the light from the firstilluminating optical system 10 is sent to the eye 60 to be measured, andthe reflected light from the eye 60 to be measured is transmitted. Thefirst light receiving part 23 included in the first light receivingoptical system 20 receives the light transmitted through the Hartmannplate 22 as the conversion member and generates a received light signal.

Besides, the first light source part 11 and the retina 61 of the eye 60to be measured form a conjugated relation. The retina 61 of the eye 60to be measured and the first light receiving part 23 are conjugate.Besides, the Hartmann plate 22 and the pupil of the eye 60 to bemeasured form a conjugated relation. Further, the first light receivingoptical system 20 forms a substantially conjugated relation with respectto the cornea 62 as the anterior eye part of the eye 60 to be measured,the pupil, and the Hartmann plate 22. That is, the front focal point ofthe afocal lens 42 is substantially coincident with the cornea 62 as theanterior eye part of the eye 60 to be measured and the pupil.

Besides, the first illuminating optical system 10 and the first lightreceiving optical system 20 are moved together so that a signal peakaccording to the reflected light at the light receiving part 23 becomesmaximum on the condition that the light flux from the first light sourcepart 11 is reflected at a point on which it is condensed. Specifically,the first illuminating optical system 10 and the first light receivingoptical system 20 are moved in a direction in which the signal peak atthe first light receiving part 23 becomes large, and are stopped at aposition where the signal peak becomes maximum. By this, the light fluxfrom the first light source part 11 is condensed on the eye 60 to bemeasured.

Besides, the lens 12 converts a diffused light of the light source 11into a parallel light. A diaphragm 14 is positioned at an opticallyconjugated position with respect to the pupil of the eye or the Hartmannplate 22. The diaphragm 14 has a diameter smaller than an effectiverange of the Hartmann plate 22, and the so-called single path aberrationmeasurement (method in which aberrations of an eye have an influence ononly the light receiving side) is established. In order to satisfy theabove, the lens 13 is disposed such that the retina conjugated point ofthe real light beam coincides with the front focal position, andfurther, in order to satisfy the conjugated relation between the lensand the pupil of the eye, it is disposed such that the rear focalposition coincides with the diaphragm 14.

Besides, after a light beam 15 comes to have a light path common to alight beam 24 by the beam splitter 45, it travels in the same way as thelight beam 24 paraxially. However, in the single path measurement, thediameters of the light beams are different from each other, and the beamdiameter of the light beam 15 is set to be rather small as compared withthe light beam 24. Specifically, the beam diameter of the light beam 15is, for example, about 1 mm at the pupil position of the eye, and thebeam diameter of the light beam 24 can be about 7 mm (incidentally, inthe drawing, the light beam 15 from the beam splitter 45 to the retina61 is omitted).

Next, the Hartmann plate 22 as the conversion member will be described.

The Hartmann plate 22 included in the first light receiving opticalsystem 20 is a wavefront conversion member for converting a reflectedlight flux into plural beams. Here, plural micro-Fresnel lenses disposedon a plane orthogonal to the optical axis apply in the Hartmann plate22. Besides, in general, with respect to the measurement object part(the eye 60 to be measured), in order to measure a sphere of the eye 60to be measured, third-order astigmatism aberrations, and other higherorder aberrations, it is necessary to perform the measurement with atleast 17 beams through the eye 60 to be measured.

Besides, the micro-Fresnel lens is an optical element, and includes, forexample, a ring with a height pitch for each wavelength, and a bladeoptimized for emission parallel to a condensing point. The micro-Fresnellens here is subjected to, for example, 8-level optical path lengthvariation employing a semiconductor fine working technique, and achievesa high condensing efficiency (for example, 98%).

Besides, the reflected light from the retina 61 of the eye 60 to bemeasured passes through the afocal lens 42 and the collimate lens 21 andis condensed on the first light receiving part 23 through the Hartmannplate 22. Accordingly, the Hartmann plate 22 includes a wavefrontconversion member for converting the reflected light flux into at least17 beams.

FIG. 2 is a structural view of an electrical system 200 of the eyeoptical characteristic measuring apparatus. The electrical system 200 ofthe eye optical characteristic measuring apparatus includes, forexample, a calculation section 210, a control section 220, a displaysection 230, a memory 240, an input section 270, a first driving section250, a second driving section 260, and a third driving section 280.Besides, the calculation section 210 can include a pupil data formationsection 215, an image data formation section 211, a judgment section212, and a correction element specifying section 123.

The calculation section 210 receives a received light signal (4)obtained from the first light receiving part 23, a received light signal(7) obtained from the second light receiving part 35, and a receivedlight signal (10) obtained from the third light receiving part 54, andperforms an arithmetical operation on the origin of coordinates,coordinate axis, movement of coordinates, rotation, pupil diameter,ocular aberrations, corneal wavefront aberrations, Zernike coefficients,aberration coefficients, visual acuity simulation, Strehl ratio (Strehlratio), phase shift (PTF, phase shift), white light MTF, Landolt's ringpattern, contrast sensitivity and the like. The processing of idealobserved analysis as proposed by Wilson Geiseler may be performed(Geisler, W. S. 1989 Psychological Review 96, pp. 267-324). Besides,signals corresponding to such calculation results are outputted to thecontrol section 220 for performing the whole control of an electricdriving system, the display section 230 and the memory 240,respectively. Incidentally, the details of the calculation section 210will be described later.

The pupil data formation section 215 forms pupil data from an anteriorocular segment image. For example, the pupil data formation section 215receives the anterior ocular segment image from the second lightreceiving part 35, calculates points on an edge of a pupil, a focalpoint, a major axis and a minor axis when the pupil is elliptic, andobtains a pupil diameter. When the pupil area shape is not circular butelliptic or is still another shape, this is specified to obtain measuredvalues used for analysis.

In correction data calculation in after-mentioned template matching orvisual acuity simulation, based on the measurement data indicating atleast wavefront aberrations of the eye to be examined and in view of acorrection element for refraction correction, the image data formationsection 211 performs the simulation of visibility of the index for eyeexamination, and forms index retinal image data. The wavefrontaberrations of the eye to be examined include higher order aberrations.That is, parameters of distributions concerning all refractions areincluded. Based on the index retinal image data formed by the image dataformation section 211, the judgment section 212 judges whether or notthe index for eye examination is seen.

Besides, the correction element specifying section 213 specifies thecorrection element to be given to the image data formation section 211.Further, based on the index retinal image data which is corrected withthe correction element specified by the correction element specifyingsection 213 and is formed by the image data formation section 211, thejudgment section 212 judges whether or not the appropriate correctionelement is specified. Besides, the correction element specifying section213 specifies a correction element based on the result of the judgmentsection 212, and repeatedly changes the correction element until thejudgment section 212 judges that it is the appropriate correctionelement. The correction element is one of or a combination of two ormore of a spherical power, an astigmatic power, and an astigmatic axisangle.

The control part 220 controls lighting and extinction of the first lightsource part 11 on the basis of the control signal from the arithmeticpart 210, or controls the first driving part 250 and the second drivingpart 260. For example, on the basis of the signals corresponding to theoperation results in the arithmetic part 210, the control part outputs asignal (1) to the first light source part 11, outputs a signal (5) tothe Placido's disk 71, outputs a signal (6) to the second light sourcepart 31, outputs a signal (8) to the third light source part 51, outputsa signal (9) to the fourth light source part 55, outputs a signal (11)to the fifth light source part 91, and outputs signals to the firstdriving part 250 and the second driving part 260.

The first driving part 250 is for moving the whole first illuminatingoptical system 10 in the optical axis direction on the basis of, forexample, the received light signal (4) inputted to the arithmetic part210 from the first light receiving part 23, and outputs a signal (2) toa not-shown suitable lens movement means and drives the lens movementmeans. By this, the first driving part 250 can perform the movement andadjustment of the first illuminating optical system 10.

The second driving part 260 is for moving the whole first lightreceiving optical system 20 in the optical axis direction on the basisof, for example, the received light signal (4) inputted to thearithmetic part 210 from the first light receiving part 23, and outputsa signal (3) to a not-shown suitable lens movement means, and drives thelens movement means. By this, the second driving part 260 can performthe movement and adjustment of the first light receiving optical system20.

The third driving section 280 is for moving a fixation index 92 of thethird illuminating optical system 90, and outputs a signal (12) to anot-shown appropriate movement means and drives the movement means. Bythis, the third driving section 280 can perform the movement andadjustment of the fixation index 92 of the third illuminating opticalsystem 90.

2. Zernike Analysis

Next, a Zernike analysis will be described. A generally known method ofcalculating Zernike coefficients C_(i) ^(2j−i) from Zernike polynomialswill be described. The Zernike coefficients C_(i) ^(2j−i) are importantparameters for grasping the optical characteristic of the subject eye 60on the basis of inclination angles of the light fluxes obtained by thefirst light receiving part 23 through the Hartmann plate 22.

Wavefront aberrations W(X, Y) of the subject eye 60 are expressed usingthe Zernike coefficients C_(i) ^(2j−i) and the Zernike polynomials Z_(i)^(2j−i) by the following expression.

$\begin{matrix}{{W\left( {X,Y} \right)} = {\sum\limits_{i = 0}^{n}{\sum\limits_{j = 0}^{i}{c_{i}^{{2j} - i}{Z_{i}^{{2j} - i}\left( {X,Y} \right)}}}}} & (1)\end{matrix}$

Where, (X, Y) denotes vertical and horizontal coordinates of theHartmann plate 22.

Besides, with respect to the wavefront aberrations W(X, Y), when thehorizontal and vertical coordinates of the first light receiving part 23are denoted by (x, y), a distance between the Hartmann plate 22 and thefirst light receiving part 23 is denoted by f, and a movement distanceof a point image received by the first light receiving part 23 isdenoted by (Δx, Δy), the following expression is established.

$\begin{matrix}{\frac{\partial{W\left( {X,Y} \right)}}{\partial X} = \frac{\Delta\; x}{f}} & (2) \\{\frac{\partial{W\left( {X,Y} \right)}}{\partial Y} = \frac{\Delta\; y}{f}} & (3)\end{matrix}$

Where, the Zernike polynomials Z_(i) ^(2j−i) are expressed by thefollowing numerical expressions (4) and (5). (More specificallyexpressions, for example, see JP-A-2002-209854.)

$\begin{matrix}{Z_{n}^{m} = {{R_{n}^{m}(r)}\left\{ \frac{\sin}{\cos} \right\}\left\{ {m\;\theta} \right\}}} & (4) \\{m > {0\mspace{14mu}\sin}} & \; \\{m \leqq {0\mspace{14mu}\cos}} & \; \\{{R_{n}^{m}(r)} = {\sum\limits_{S = 0}^{{({n - m})}/2}{\left( {- 1} \right)^{S}\frac{\left( {n - S} \right)!}{{S!}{\left\{ {{\frac{1}{2}\left( {n - m} \right)} - S} \right\}!}{\left\{ {{\frac{1}{2}\left( {n + m} \right)} - S} \right\}!}}r^{m}}}} & (5)\end{matrix}$

Incidentally, with respect to the Zernike coefficients C_(i) ^(2j−i),specific values can be obtained by minimizing the squared errorexpressed by the following numerical expression.

$\begin{matrix}{{S(x)} = {\sum\limits_{i = 1}^{{data}\mspace{14mu}{number}}\left\lbrack {\left\{ {\frac{\partial{W\left( {X_{i},Y_{i}} \right)}}{\partial X} - \frac{\Delta\; x_{i}}{f}} \right\}^{2} + \left\{ {\frac{\partial{W\left( {X_{i},Y_{i}} \right)}}{\partial Y} - \frac{\Delta\; y_{i}}{f}} \right\}^{2}} \right\rbrack}} & (6)\end{matrix}$

Where, W(X, Y): wavefront aberrations, (X, Y): Hartmann platecoordinates, (Δx, Δy): a movement distance of a point image received bythe first light receiving part 23, f: a distance between the Hartmannplate 22 and the first light receiving part 23.

The arithmetic part 210 calculates the Zernike coefficients C_(i)^(2j−i), and uses this to obtain eye optical characteristics such asspherical aberrations, coma aberrations, and astigmatism aberrations.

(Normalization of Pupil Diameter)

A Zernike polynomial always indicates a shape in a circle with a radiusof 1, and when Zernike analysis is performed at a certain pupil diameter(pupil diameter), normalization is performed with the pupil radius. Forexample, when the center coordinate of the pupil with the pupil radiusr_(p) is made (0, 0), a point P(X, Y) in the pupil is made P(X/r_(p),Y/r_(p)) when the Zernike analysis is performed. When the barycentricpoint of a spot of a Hartmann image is P, a reference lattice pointP_(ref) (X_(ref), Y_(ref)) corresponding to this point is madeP_(ref)(X_(ref)/r_(p), Y_(ref)/r_(p)), and a movement distance of apoint image is obtained, and the Zernike coefficients are calculated.The actual wavefront (wavefront in which the coordinates are notnormalized) W(X, Y) is expressed by a following expression.

$\begin{matrix}\begin{matrix}{{W\left( {X,Y} \right)} = {\sum\limits_{i = 0}^{n}{\sum\limits_{j = 0}^{i}{c_{i}^{{2j} - 1}{Z_{i}^{{2j} - 1}\left( {{X/r_{p}},{Y/r_{p}}} \right)}}}}} \\{= {\sum\limits_{i = 0}^{n}{\sum\limits_{j = 0}^{i}{c_{i}^{{2j} - 1}{Z_{i}^{{2j} - 1}\left( {x_{s},y_{s}} \right)}}}}}\end{matrix} & (7)\end{matrix}$Where, (X, Y): coordinates not normalized, (x_(s), y_(s)): coordinatesnormalized.3. Landolt's Ring

FIG. 3 is an explanatory view of a Landolt's ring.

Hereinafter, preparation of data of a luminous distribution functionLand(x, y) of the Landolt's ring will be described. FIG. 3 showsLandolt's ring of high contrast in upper stand, and Landolt's ring oflow contrast in lower stand.

The Landolt's ring is expressed by the reciprocal of a recognizableminimum visual angle, and the ability to be capable of recognizing avisual angle of one minute is called visual acuity of 20/20. Forexample, if the recognizable minimum visual angle is 2 minutes, thevisual acuity is defined as 20/40, and if 10 minutes, the visual acuityis defined as 20/200. In general, the Landolt's ring uses, as an index,a ring in which a gap being ⅕ of the size of the outside ring isprovided as shown in the drawing.

When the visual acuity is V, the size d of the Landolt's ring projectedon the retina is calculated by

$\begin{matrix}{d = {5 \times {2 \cdot R}\;{\tan\left( {\frac{1}{60 \cdot V} \times \frac{1}{2}} \right)}}} & (8)\end{matrix}$(R: a distance between a pupil and an image point (retina))

On the basis of this expression and the definition of the Landolt'sring, a black portion of the Landolt's ring is made 0 (or 1), a whiteportion thereof is made 1 (or 0), and the luminous distribution functionLand(x, y) of the Landolt's ring is prepared. The data of the preparedluminous distribution function Land(x, y) is stored in the memory 240,is read out by the arithmetic part 210, and is set correspondingly topredetermined visual acuity.

A high contrast original image is such that for example, the contrast ofthe black portion and the white portion of a Landolt's ring is 100% (forexample, the white is 0 and the black is 1), or the figure portion of aLandolt's ring is black (10 cd/m² or less) and the background is white(100 cd/m²) and the actual contrast is 90% or more. Here, the contrastis such that Michelson contrast (I white−I black)/(I white+I black) isexpressed by %. On the other hand, as a low contrast original image, onein which the contrast of the black portion and the white portion of aLandolt's ring is 10% (for example, the white is 0 and the black is 0.1)can be used. These contrasts have an accuracy of approximately ±1%.Incidentally, in addition to this example, an appropriate contrastoriginal image may be used. As a luminance distribution function Land(x, y) stored in the memory 240, a high contrast one and a low contrastone are respectively formed and are stored.

4. Ophthalmic Data Measuring Method

FIG. 4 is a flowchart of ophthalmic data measurement.

First, the eye optical characteristic measuring apparatus makesalignment of X, Y and Z axes of the pupil position of the eye 60 to bemeasured (S101). Next, the measuring apparatus moves the origin of amovable section (S103). For example, the Hartmann plate 22, thePlacido's disk 71 or the like is set to zero diopter. The calculationsection 210 measures the data of the eye optical system, such as thepupil diameter, ocular aberrations and Zernike coefficients, on thebasis of the measured received light signals (4), (7) and/or (10)(S105). The calculation section 210 performs a visual acuity simulationor a correction image simulation (S107).

In the visual acuity simulation, for example, at step S107, thecalculation section 210 uses, as an evaluation parameter indicating thequality of visibility by the eye 60 to be examined, a comparison resultbetween a simulation result of visibility of the index for eyeexamination and a predetermined template and/or an MTF (ModulationTransfer Function) indicating the transfer characteristic of the eye tobe examined, and estimates the visual acuity of the eye to be examinedor the sensitivity in accordance with the evaluation parameter.Incidentally, as the visual acuity, the index for eye examination issuitably set, so that the high contrast visual acuity and low contrastvisual acuity can be estimated. Besides, the calculation section 210estimates optical characteristics such as the MTF of the eye to beexamined and the point spread function (PSF).

Besides, in the correction image simulation, for example, thecalculation section 210 obtains appropriate correction data while usingone of or two or more of the Strehl ratio, the PTF, and the MTF(Modulation Transfer Function) as the evaluation parameter indicatingthe quality of visibility by the eye 60 to be measured. Besides, thecalculation section 210 may obtain appropriate correction data by, forexample, performing the simulation of visibility of the index for eyeexamination and using the comparison result to a predetermined templateas an evaluation parameter.

Incidentally, the details of step S105 and S107 will be described later.The calculation section 210 outputs data to the display section 230 andthe memory 240 (S109). Incidentally, in the case where data output hasalready been made in the former processing, the processing of step S109may be omitted.

FIG. 5 is a sub-flowchart concerning calculation of the pupil diameterat step S105 and measurement of data of the eye optical system. Besides,FIG. 6 is an explanatory view of pupil diameter calculation.

First, the calculation section 210 acquires a Hartmann image and ananterior ocular segment image from the first light receiving part 20 andthe second light receiving part 35 (S601). The calculation section 210causes the fifth light source part 91 to illuminate the eye 60 to bemeasured in an illumination state of a desired environmental condition(observation condition), and acquires the Hartmann image and theanterior ocular segment image from the first light receiving part 20 andthe second light receiving part 35. For example, the calculation section210 causes the display section 230 to display instructions to select anenvironmental condition under which the visual acuity or sensitivity isestimated, and the selected environmental condition may be inputted fromthe input section 270. The environmental condition includes, forexample, “seeing in the daytime”, “seeing in the twilight”“seeing in aroom (under a fluorescent lamp)”, “seeing in the nighttime”, “normalvisual acuity measurement” and the like. Next, the calculation section210 refers to, for example, a table which is previously stored in thememory 240 and in which the environmental conditions and theillumination states correspond to each other, and acquires theillumination state corresponding to the inputted environmentalcondition. The illumination states under the respective environmentalconditions can be made such that for example, the case of “normal visualacuity measurement” is 50 [1×], “seeing in the daytime” is 100000 [1×],and “in a room (fluorescent lamp)” is 2000 [1×]. Incidentally, withrespect to these values, an appropriate value corresponding to theenvironmental condition can be used. As the environment, it is desirableto use a fixation target larger than a normal one. Here, although theeye 60 to be examined is illuminated in the illumination state of thedesired environmental condition by the fifth light source part 91, astructure may be made such that the illumination state is formed byusing the surrounding illumination of the eye to be examined or thebackground illumination.

The calculation section 210 outputs a signal (11) corresponding to theacquired illumination state to the fifth light source part 91 throughthe control section 220, and causes the eye 60 to be measured to beilluminated. Besides, the calculation section 210 sequentially changesthe illumination state from a dark one to a bright one, and can acquirethe Hartmann images and anterior ocular segment images in the pluralillumination states.

Incidentally, the calculation section 210 may omit step S601, and readsHartmann image data previously measured and stored in the memory 240,and pupil data including one of the anterior ocular segment image, thepupil shape such as points on the pupil edge, and pupil diameter.Besides, for example, the calculation section 210 may acquire theanterior ocular segment image by reading, as the pupil data in anelectric carte, photographic data photographed in the past and stored inthe memory 240 from the memory.

Next, based on the acquired anterior ocular segment image, thecalculation section 210 detects, for example, 36 (n=36) points P_(i)(i=1 to n) on the edge of the pupil (S603). The calculation section 210detects the change (light and shade on the image) of the acquired lightamount of the anterior ocular segment image by a method of imageprocessing, and can obtain points on the edge of the pupil. In FIG. 6,the detection points P_(i) are points indicated by marks of “+”.

Next, the calculation section 210 performs elliptic fitting which isfittest to the detected points on the edge of the pupil (S605). First,the calculation section 210 obtains the focal points (points F1 and F2in FIG. 6) of the ellipse. For example, the calculation section 210reads the coordinates of two points previously set as the initial valuesof the focal points from the memory 240. Next, the calculation section210 obtains distances from the detection point P_(i) to the two readpoints, and the sum of the distances is made L_(i). The calculationsection 210 obtains the sum L_(i) of the distances concerning all thedetection points Pi, and obtains a mean value A of Li. Further, thecalculation section 210 uses a method of the least square approximationor the like to calculate two points where a square error Se of the sumL_(i) of the distance and the mean value A expressed by a followingexpression becomes minimum, and consequently, the focal points of theellipse can be obtained.

$\begin{matrix}{\;{S_{e} = {\sum\limits_{i = 1}^{n}\left( {L_{i} - A} \right)^{2}}}} & (9)\end{matrix}$Where, Li: the sum of distances from the point P_(i) on the edge to thetwo points F1 and F2, A: the mean value of L_(i) at the respectivepoints on the edge, n: the number of detected points on the edge.Incidentally, the focal points of the ellipse may be obtained by anappropriate method other than this.

Next, the calculation section 210 obtains the sum L of distances fromone point on the ellipse to the focal points. Incidentally, thecalculation section 210 may make the foregoing mean value A the sum L ofthe distances from one point on the ellipse to the focal points. Next,the calculation section 210 calculates the pupil diameter from thelength (major axis) of the long axis of the ellipse and the length(minor axis) of the short axis (S607). The length 2 a of the long axisand the length 2 b of the short axis can be expressed by followingexpressions.

$\begin{matrix}\begin{matrix}{{2a} = L} \\{{2b} = {2\sqrt{\left( \frac{L}{2} \right)^{2} - c^{2}}}} \\{\mspace{25mu}{= {2\sqrt{\frac{L^{2}}{4} - \frac{\left( {{x2} - {x1}} \right)^{2} + \left( {{y2} - {y1}} \right)^{2}}{4}}}}} \\{\mspace{25mu}{= \sqrt{L^{2} - \left( {{x2} - {x1}} \right)^{2} - \left( {{y2} - {y1}} \right)^{2}}}}\end{matrix} & (10)\end{matrix}$Where, L: the sum of distances from a point on the edge to the focalpoints, (x1, y1), (x2, y2): the focal points of the ellipse. When it isassumed that the pupil diameter d_(p) is, for example, the mean value ofthe length 2 a of the long axis and the length 2 b of the short axis, itis expressed by a following expression.

$\begin{matrix}\begin{matrix}{d_{p} = {a + b}} \\{= {\frac{1}{2}\left( {L + \sqrt{L^{2} - \left( {{x2} - {x1}} \right)^{2} - \left( {{y2} - {y1}} \right)^{2}}} \right)}}\end{matrix} & (11)\end{matrix}$Incidentally, instead of making the mean value the pupil diameter, anappropriate value based on the length 2 a of the long axis and thelength 2 b of the short axis, such as the length of the short axis, thelength of the long axis, or an intermediate value of the lengths of theshort axis and the long axis, may be used.

The calculation section 210 obtains the pupil center position based on,for example, the focal points of the ellipse and/or the lengths of thelong axis and the short axis, and further obtains or specifies thelimbus center, and may calculate the shift amount of the pupil centerposition such as the shift amount from the limbus center. Besides, thecalculation section 210 makes the calculated shift amount correspond tothe pupil diameter and stores it into the memory 240.

Incidentally, the calculation section 210 may adjust the brightness ofthe fifth light source part 91 to produce the illumination state inwhich the pupil diameter in the environment desired by the subjectiveeye (for example, in an office, in a classroom, driving in the night,etc.) is obtained, in addition to the illumination state in which thepupil diameter in the daytime is obtained. Besides, pupil diameters inthe above environments are previously measured and may be used toperform the analysis. By this, the optimum prescription value in theenvironment desired by the subjective eye can be analyzed. Incidentally,the calculation section 210 may read the measured data and the pupildiameter previously stored in the memory 240 instead of the processingof steps S601 to S607.

The calculation section 210 calculates eye optical system data based onthe pupil diameter and the Hartmann image (S609). First, the calculationsection 210 detects barycenter points of the respective spots from theHartmann image acquired at step S601. Next, the calculation section 210normalizes the barycenter point coordinates detected when the pupilcenter is made the origin by the pupil radius r_(p). Here, the pupilradius r_(p)=pupil diameter d_(p)/2. That is, the calculation section210 sets the barycenter point P_(s)(X, Y) in the range of the pupildiameter to P_(s)(X/r_(p), Y/r_(p)), and when the barycenter point ofthe spot of the Hartmann image is P_(s) the reference lattice pointP_(ref) (X_(ref), Y_(ref)) corresponding to this point is madeP_(ref)(x_(ref)/r_(p), y_(ref)/r_(p)). The actual wavefront (wavefrontin which the coordinates are not normalized) W(X, Y) is expressed by afollowing expression.

$\begin{matrix}\begin{matrix}{{W\left( {X,Y} \right)} = {\sum\limits_{i = 0}^{n}{\sum\limits_{j = 0}^{i}{c_{i}^{{2j} - 1}{Z_{i}^{{2j} - 1}\left( {{X/r_{p}},{Y/r_{p}}} \right)}}}}} \\{= {\sum\limits_{i = 0}^{n}{\sum\limits_{j = 0}^{i}{c_{i}^{{2j} - 1}{Z_{i}^{{2j} - 1}\left( {x_{s},y_{s}} \right)}}}}}\end{matrix} & (12)\end{matrix}$Where, (X, Y): coordinates not normalized, (x_(s), y_(s)): coordinatesnormalized.

The calculation section 210 uses the normalized coordinates, andcalculates the eye optical system data such as the Zernike coefficientsand ocular aberrations. Besides, the calculation section 210 stores datainto the memory 240 at an appropriate timing.

5. Visual Acuity Simulation

5-1. First Flowchart (Spherical Power Correction) of Visual AcuitySimulation

FIG. 7 shows a first flowchart of visual acuity simulation. FIG. 7 showsthe flowchart in which retinal image simulation is performed, acorrection spherical power is obtained so that a Landolt's ring can bedetected, and the visual acuity at the time of the correction isestimated. Incidentally, in the following respective flowcharts, atsteps denoted by the same reference characters, the same processing isperformed.

First, the calculation section 210 calculates a tentative sphericalpower Sr (S1401). As the tentative spherical power Sr, for example, arefractive value or a value calculated from wavefront aberrations may beused, or a value previously stored in the memory 240 or a value inputtedfrom the input section 270 may be used.

Next, the calculation section 210 specifies a spherical power Ss forsimulation (S1451). Normally, Ss is specified to be a weak correctionwith respect to Sr (for example, Ss=Sr+5D). The calculation section 210specifies the Landolt's ring of a previously determined visual acuity Vs(for example, Vs=0.1) (S1453). At this time, first, the calculationsection 210 specifies which of high contrast visual acuity and lowcontrast visual acuity is estimated. For example, the calculationsection 210 may specify the high contrast or low contrast in accordancewith the input from the input section 270 or the specificationpreviously stored in the memory 240. In accordance with thespecification, the calculation section 210 specifies the Landolt's ringof the high contrast or low contrast corresponding to the previouslydetermined visual acuity Vs.

The image data formation section 211 of the calculation section 210performs the simulation of a Landolt's ring retinal image to obtainindex image data (S1405). Here, the image data formation section 211performs it with respect to the Landolt's ring in a previouslydetermined direction (for example, a gap of the ring is provided in anupper, lower, right or left direction). That is, in accordance with thewavefront aberrations measured at step S105, the image data formationsection 211 obtains index image data indicating the visibility of theLandolt's ring by simulation. The specific processing of this simulationwill be described later.

Next, the judgment section 212 of the calculation section 210 performsLandolt's ring template matching (S1407). The judgment section 212performs the template matching between the index image data obtained bythe simulation and the Landolt's ring in a certain direction, and storesthe direction at that time and the score n indicating a coincidencedegree into the memory 240. The specific processing thereof will bedescribed later.

The judgment section 212 judges whether the template matching isperformed in all directions (S1409). Here, in the case of No, advance ismade to step S1407, and the processing is repeated until the templatematching is performed in all the directions. On the other hand, in thecase of Yes at step S1409, the judgment section 212 judges whether thehighest score nh of the score n matches the direction of the Landolt'sring of the index image data simulated at step S1405 (S1411). Here, inthe case of Yes, the judgment section 212 judges whether the score nh ishigher than a previously determined threshold value in the memory 240 orthe like (S1413). Incidentally, as the threshold value (threshold valueby which a judgment is made as to whether the Landolt's ring can bediscriminated), for example, a value obtained by comparison withsubjective values of many normal eyes in the past can be used.

In the case of No at step S1411 or S1413, the judgment section 212judges whether Ss exceeds a previously determined allowable value (forexample, Sr-5D) (S1415). Here, in the case of No, the correction elementspecifying section 213 sets the correction element of Ss to be slightlystrong (for example, Ss-0.25D) (S1417), and the image data formationsection 211 performs the simulation of the Landolt's ring retinal imagebased on this correction element. The calculation section 210 performsthe processing subsequent to step S1407 concerning the index image dataobtained by this simulation. On the other hand, in the case of Yes atstep S1415, the judgment section 212 judges that the Landolt's ring cannot be detected (S1419), and stores the direction at this time and thatthe detection could not be made in this direction into the memory 240.

After step S1419 or in the case of Yes at step S1413, the judgmentsection 212 judges whether simulation has been performed in alldirections of the Landolt's ring (S1421). Here, in the case of No,return is made to step S1405, and the calculation section 210 repeatsthe foregoing processing in all directions. On the other hand, in thecase of Yes at step S1421, the judgment section 212 judges whetherdetection could be made in number equal to or more than half ofspecified number of directions (S1455).

In the case of Yes at step S1455, the correction element specifyingsection 213 specifies S=Ss and V=Vs, and specifies the Landolt's ring ofvisual acuity Vs=Vs+0.1 (S1457). At this time, as the specifiedLandolt's ring, in accordance with the specification at step S1453, theLandolt's ring of the high contrast or low contrast is specified.Thereafter, advance is made to step S1405, the image data formationsection 211 performs the simulation of the retinal image based on thespecified correction element and Landolt's ring to obtain index imagedata, and performs the processing subsequent to step S1407. On the otherhand, in the case of No at step S1455, the calculation section 210performs data output (S1423). That is, the calculation section 210displays the visual acuity V at this time, the spherical power S=Ss, thedirection of the Landolt's ring which could be detected, simulationresult and the like on the display section 230 and stores them into thememory 240. Incidentally, the calculation section 210 may use decimalvisual acuity as the visual acuity, or may use logMAR (log Minimum AngleResolution) visual acuity. The logMAR visual acuity is the visual acuityexpressed by the logarithm of minimum vision. Incidentally, the data tobe displayed and stored are not limited to the foregoing, andappropriate data can be displayed and stored. Besides, it may besuitably selected among the foregoing data. For example, data except thevisual acuity V may be displayed.

FIG. 8 is a flowchart of the simulation of a retinal image at the abovestep S1405. First, the calculation section 210 calculates a pupilfunction f(x, y) based on the wavefront aberration W(X, Y) obtained atstep S105 of FIG. 4 and the specified correction element by a followingexpression (S204).f(x,y)=e ^(ikW(X,Y))  (13)

The calculation section 210 refers to the memory 240 and calculates theluminance distribution function Land(x, y) of the Landolt's ring (or anarbitrary image) (S205). The calculation section 210 performs thetwo-dimensional Fourier transform of Land(x, y) to obtain a spatialfrequency distribution FR(u, v) (S207). The calculation section 210calculates a spatial frequency distribution OTF of the eye based on thepupil function, and obtains a frequency distribution OR(u, v) afterpassing through the eye optical system by multiplying the spatialfrequency distribution FR(u, v) of the Landolt's ring (or arbitraryimage) by the spatial frequency distribution OTF(u, v) of the eye (S209)as follows.FR(u, v)×OTF(u, v)→OR(u, v)Incidentally, the specific calculation method of the OTF will bedescribed later.

Next, the calculation section 210 performs the two-dimensional inverseFourier transform of OR(u, v) to obtain the luminance distribution imageLandImage (X, Y) of the Landolt's ring (or arbitrary image) (S211).

FIG. 9 is an explanatory view of template matching of step S1407. Asshown in the drawing, a template image (lower drawing) is specifiedcorrespondingly to the Landolt's ring original image (upper drawing),and the template image as stated above is stored in the memory 240correspondingly to an identifier indicating the size of the Landolt'sring. Although the template image is such that in this example, b ismade b=1.5a, the number of pixels of the Landolt's ring is N1, the pixelnumber is 1, the number of pixels of a blurred point image part aroundthe Landolt's ring is N2, and the pixel value is −N1/N2, it is notlimited to this but can be suitably specified. Besides, although theLandolt's ring original image shown on the upper part of FIG. 9 showsthe Landolt's ring original image of high contrast, also in the casewhere the Landolt's ring original image of low contrast is used, asimilar template can be used.

FIG. 10 shows a flowchart of the Landolt's ring template matching atstep S1407.

The calculation section 210 reads the template image from the memory 240in accordance with the size of the specified Landolt's ring, and obtainsthe spatial frequency distribution Temp(x, y) thereof (S1301). Next, thecalculation section 210 obtains the two-dimensional Fourier transformFT(u, v) of Temp(x, y) (S1303). The calculation section 210 obtains thetwo-dimensional Fourier transform OR(u, v) of the spatial frequencydistribution of the index image data by the simulation of the retinalimage, and multiplies OR(u, v) by the spatial frequency distributionFT(u, v) of the template as indicated by a following expression, andobtains OTmp(u, v) (S1305).OR(u, v)×FT(u, v)→OTmp(u, v)

The calculation section 210 performs the two-dimensional inverse Fouriertransform of OTmp(u, v) to obtain TmpIm(X, Y) (complex matrix of 4a×4a)(S1307). The calculation section 210 acquires the maximum value of theabsolute value of TmpIm(X, Y) to obtain the score n (S1309).

By taking such a correlation, when the simulation index image is closeto the original image, the score is high, and in the case of blur, thescore becomes low according to that.

5-2. Second Flowchart (Astigmatic Correction −1) of Visual AcuitySimulation

FIGS. 11 and 12 show second flowcharts (1) and (2) of the visual acuitysimulation. FIGS. 11 and 12 show the flowcharts in which the simulationof a retinal image is performed, a correction astigmatic axis A and anastigmatic power C are obtained so that the Landolt's ring can bedetected, and the visual acuity at the time of the correction isestimated. This example shows a case where the astigmatic power has anegative value.

Similarly to step S1401, the calculation section 210 calculates atentative spherical power Sr (S1401). By specifying the tentativespherical power Sr, in order to avoid the retina from approaching thefront focal line relatively to the rear focal line, it may be set to beslightly weaker correction than Sr specified at step S1401 (for example,Sr→Sr+0.5D). Alternatively, what is obtained by subtracting therefractive value or ½ of the astigmatic power Cs calculated from thewavefront aberrations from S obtained as described above, or what isspecified to be slightly weaker correction than them may be used. Next,the calculation section 210 specifies the astigmatic power Cs forsimulation (S1501). For example, Cs may be obtained by using therefractive value or the astigmatic power C calculated from the wavefrontaberrations, or a correspondence table storing Cs corresponding tocorrection elements such as S or C or Zernike coefficients is stored inthe memory 240, and it may be obtained by referring to that. Next, thecalculation section 210 specifies the Landolt's ring of visual acuity Vs(for example, Vs=0.1) similarly to the above (S1453).

At steps S1405 to S1413, similarly to the above, the calculation section210 performs the processing such as the Landolt's ring retinal imagesimulation and Landolt's ring template matching. In the case of No atstep S1411 or S1413, the judgment part 212 judges that the Landolt'sring can not be detected, and stores the direction at this time and thatthe detection could not be made in this direction into the memory 240(S1419). After step S1419 or in the case of Yes at step S1413, similarlyto the above, the calculation section 210 performs the processing ofstep S1421 and S1455.

At step S1455, in the case where it is judged that detection could bemade in number of directions equal to or more than half of specifiednumber of direction, the calculation section 210 stores the specifiedcorrection element into the memory 240 (S1503). Next, the correctionelement specifying section 213 specifies V=Vs, and specifies theLandolt's ring of visual acuity Vs=Vs+0.1 (S1505). At this time, withrespect to the Landolt's ring to be specified, in accordance with thespecification at step S1453, the Landolt's ring of high contrast or lowcontrast is specified. Thereafter, advance is made to S1405, and theimage data formation section 211 performs the retinal image simulationbased on the specified correction element and the Landolt's ring toobtain index image data, and performs the processing subsequent to stepS1407.

On the other hand, in the case of No at step S1455, the judgment section212 judges whether the simulation is performed in all astigmatic axisangle directions (0 to 180) (S1507). Here, in the case of No, thecorrection element specifying section 213 rotates the astigmatic axisangle As (for example, As=As+5) (S1509). Thereafter, advance is made tostep S1453, and the processing subsequent to step S1453 is repeatedlyperformed.

Next, referring to FIG. 12, in the case where the judgment section 212makes a judgment of Yes at step S1507, the correction element specifyingsection 213 of the calculation section 210 substitutes, as theastigmatic axis angle A, As at the time when the visual acuity V islargest (S1511). Incidentally, when there are plural As at the time whenit is largest, one at which the number of Landolt's rings which could bedetected by the visual acuity V is largest is specified as theastigmatic axis angle A, and further, when there are plural such As, oneis specified at which the sum of nh in the direction in which detectionby the visual acuity V could be made becomes maximum. By this, theastigmatic axis angle A is determined.

At steps S1453, and S1405 to S1413, as described in the aboveembodiment, based on the specified Sr, Cs and A, the calculation section210 performs the respective processings such as the Landolt's ringretinal image simulation and the Landolt's ring template matching.

In the case of No at step S1411 or S1413, the judgment section 212judges whether Cs exceeds a previously determined allowable value (forexample, Cs-10D) (S1515). Here, in the case of No, the correctionelement specifying section 213 specifies the correction element of Cs tobe slightly strong (for example, Cs-0.25D) (S1517), the image dataformation section 211 performs the Landolt's ring retinal imagesimulation based on this correction element (S1405). The calculationsection 210 repeatedly performs the processing subsequent to step S1407with respect to the index image data obtained by this simulation. On theother hand, in the case of Yes at step S1515, the judgment section 212judges that the Landolt's ring can not be detected (S1419), and storesthe direction at this time and that the detection could not be made inthis direction into the memory 240.

After step S1419 or in the case of Yes at step S1413, similarly to theabove, the calculation section 210 performs the processing of step S1421and S1455. In the case of Yes at step S1455, the calculation section 210performs the processing of step S1503 and S1505. The processing of therespective steps is the same as the above. Thereafter, advance is madeto step S1405, and the image data formation section 211 performs theretinal image simulation based on the specified correction element andthe Landolt's ring to obtain the index image data, and performs theprocessing subsequent to step S1407.

On the other hand, in the case of No at step S1455, the calculationsection 210 performs the data output (S1423). That is, the calculationsection 210 displays the visual acuity V at this time, the astigmaticpower C=Cs, the astigmatic axis A, the spherical power S=Sr, thedirection in which detection could be made, the simulation result andthe like on the display section 230 and stores them in the memory 240.

5-3. Third Flowchart (Astigmatic Correction −2) of Visual AcuitySimulation

FIG. 13 shows a third flowchart of the visual acuity simulation. FIG. 13shows the flowchart in which the MTF is used as an evaluation parameterto obtain the astigmatic axis A and the astigmatic power C, and thevisual acuity at the time of the correction is estimated.

In step S1401, as described above, the arithmetic part 210 calculates atentative spherical power Sr. Then, the arithmetic part 210 initiallyspecifies an astigmatic power Cs and the angle As of an astigmatic axis,both of which are astigmatic components, and a comparison numeral Mh(S1571). These values may be stored in advance in the memory 240, or maybe input through the input part. The arithmetic part 210 initiallyspecifies, for example, Cs=0, As=0, and Mh=0.

The arithmetic part 210 calculates the MTF (modulation transferfunction) (S1573) according to the wavefront aberrations obtainedbefore. A specific MTF calculation method will be described later. Thearithmetic part 210 calculates a comparison numeral M from an MTFcross-section at the specified angle As of the astigmatic axis (S1575).As the comparison numeral M, the total sum of MTF values, an MTFcross-section, or the sum of 3, 6, 12, and 18 cpd, for example, can beused. The arithmetic part 210 stores currently set As and M in thememory 240.

The determination part 212 of the arithmetic part 210 determines whetherM≧Mh (S1577). If no, the processing proceeds to step S1581. If yes, thecorrection-factor setting part 213 of the arithmetic part 210 sets Mh=Mand A=As (S1579). Then, the determination part 212 determines whether Asis 180 or larger (S1581). If no, the correction-factor setting part 213rotates the angle As of the astigmatic axis (for example, As=As+5)(S1509). Then, the arithmetic part 210 goes back to step S1575 andrepeats the processes to obtain the maximum value of M in an axis-anglerange of 0 to 180 degrees and the angle As (weak main longitude line orstrong main longitude line) of the astigmatic axis equal to thedirection where the maximum value of M is obtained.

If yes in step S1581, in other words, if the angle A of the astigmaticaxis is obtained, the arithmetic part 210 calculates the MTF accordingto the astigmatic components Cs and As=A. The arithmetic part 210further calculates the comparison numeral M from each MTF cross-sectionat 0 to 180 degrees (for example, at an interval of 5 degrees).

The determination part 212 determines whether the calculated Ms arealmost equal at the angles (S1589). For example, it can be determined bydetermining whether the difference between the maximum value of M andthe minimum value of M is smaller than a predetermined threshold. If noin step S1589, the arithmetic part 210 slightly changes the astigmaticpower Cs (for example, Cs=Cs-0.25) (S1591), and the processes of stepS1585 and subsequent steps are repeated. If yes in step S1589, thearithmetic part 210 specifies C=Cs (S1593).

The calculation section 210 estimates the visual acuity after thecorrection based on the obtained astigmatic power C and the astigmaticaxis angle A (S1594). For example, the calculation section 210 performsthe processing of a fourth flowchart described later to estimate thevisual acuity after the correction. Incidentally, instead of estimatingthe visual acuity or in addition to the estimation of the visual acuity,the calculation section 210 may obtain the contrast sensitivity.

The calculation section 210 stores the obtained astigmatic power C andthe astigmatic axis angle A into the memory 240 and displays them on thedisplay section 230 as the need arises (S1595).

5-4. Visual Acuity Estimation

FIG. 14 is a fourth flowchart of the visual acuity simulation of stepS107. Besides, the flowchart shown in FIG. 14 is also a sub-flowchart ofthe foregoing step S1594. First, the calculation section 210 specifiescorrection data for simulation (S1452). For example, the calculationsection 210 can use, as the correction data, a value calculated based onthe refractive value or wavefront aberrations, or the spherical power Sobtained as stated above, the astigmatic power C, or the astigmatic axisangle A. Besides, by setting the respective elements of the correctiondata to be 0, the calculation section 210 can estimate the visual acuityin the environment of the subjective eye when the correction is notmade. Besides, for example, the calculation section 210 may specify theastigmatic power C, the astigmatic axis angle A, and/or the sphericalpower correction S, which are obtained by performing the processing ofthe foregoing flowchart. Since the processing of each step subsequent tostep S1453 is the same as the processing denoted by the same referencecharacter in the flowcharts shown in FIGS. 7 and 11, the detaileddescription will be omitted.

5-5. Contrast Sensitivity

The calculation section 210 can calculate contrast sensitivity as thevisual acuity simulation of step S107. The calculation section 210obtains Mopt(r, s) of the eye optical system based on the wavefrontaberrations, and calculates the contrast sensitivity based on theobtained MTF. Besides, the calculation section 210 displays thecalculated contrast sensitivity on the display section 230 or stores itinto the memory 240. Incidentally, the contrast sensitivity is not onlycalculated in the processing of step S107, but also can be calculatedduring the processing of the first to fourth flowcharts and can bedisplayed.

(MTF Calculation)

First, the calculation of the MTF (Modulation transfer function) will bedescribed.

The MTF is an index indicating the transfer characteristic of thespatial frequency, and is widely used to express the performance of anoptical system. In this MTF, visibility can be predicted by obtaining,for example, the transfer characteristic for 0 to 100 sinusoidal graylattices per degree. In this embodiment, as described below, amonochromatic MTF may be used or a white MTF may be used.

First, the monochromatic MTF is calculated from the wavefront aberrationW(x, y). Incidentally, W(x, y) is an input value (measured value), andwith respect to the corneal aberrations, the corneal wavefrontaberrations obtained from the cornea shape can also be used.

When the monochromatic MTF is obtained, the calculation section 210obtains the pupil function f(x, y) from the wavefront aberrations asdescribed below.f(x, y)=e ^(ikW(x, y))(i: imaginary number, k: wave number vector (2π/λ), λ: wavelength)At this time, in view of the Stiles-Crawford effect, (e^(−arp))² (a is,for example, approximately 0.05) may be multiplied. Here, r_(p) is theradius of the pupil.

The calculation section 210 performs the Fourier transform of this pupilfunction f(x, y) to obtain an amplitude distribution U(u, v) of pointimages as indicated by a following expression.

$\begin{matrix}{{{Amplitude}\mspace{20mu}{U\left( {u,v} \right)}} = {\underset{- \infty}{\overset{\infty}{\int\int}}{f\left( {x,y} \right)}\;{\exp\left\lbrack {{- \frac{\mathbb{i}}{R}}\frac{2\;\pi}{\lambda}\left( {{u\; x} + {v\; y}} \right)} \right\rbrack}\;{\mathbb{d}x}{\mathbb{d}y}}} & (14)\end{matrix}$

-   (λ: wavelength-   R: distance from the pupil to an image point (retina)-   (u, v): coordinate value in a plane perpendicular to the optical    axis while the image point O is made the origin-   (x, y): coordinate value in the pupil plane)    The calculation section 210 multiplies U(u, v) by its complex    conjugate and obtains I(u, v) as the point spread function (PSF) by    a following expression.    I(u,v)=U(u, v)U*(u, v)    Next, the calculation section 210 performs the Fourier transform (or    autocorrelation) of PSF to perform normalization, and obtains OTF.

$\begin{matrix}{{{R\left( {r,s} \right)} = {\underset{- \infty}{\overset{\infty}{\int\int}}{I\left( {u,v} \right)}\;{\mathbb{e}}^{{- {\mathbb{i}}}\; 2\;\pi\;{({{r\; u} + {s\; v}})}}{\mathbb{d}u}\;{\mathbb{d}{v\left( {r,{s\text{:}\mspace{20mu}{variables}\mspace{14mu}{in}\mspace{14mu}{spatial}\mspace{14mu}{frequency}\mspace{14mu}{area}}} \right)}}}}\text{}{{OTF} = \frac{R\left( {r,s} \right)}{R\left( {0,0} \right)}}} & (15)\end{matrix}$Besides, since the magnitude of the OTF is the MTF,MTF(r, s)=|OTF(u, v)|is established.

The white-color MTF is calculated from the single-color MTF, obtained asdescribed above.

To obtain the white-color MTF, the MTF is weighted at each wavelengthand added. Since the above-described MTF has a different value at eachwavelength, the MTF can be expressed in the following way when the MTFat a wavelength λ is indicated by MTF_(λ).

$\begin{matrix}{{{MTF}\left( {r,s} \right)} = \frac{\int{\omega_{\lambda}{{MTF}_{\lambda}\left( {r,s} \right)}\;{\mathbb{d}\lambda}}}{\int{\omega_{\lambda}\;{\mathbb{d}\lambda}}}} & (16)\end{matrix}$

The MTF is highly weighted at visible-light wavelengths, and thecalculation is made.

More specifically, the MTF is obtained in the following way when it isassumed, for example, that the three primary colors (R, G, and B) arespecified such that red light has a wavelength of 656.27 nm with aweight of 1, green light has a wavelength of 587.56 nm with a weight of2, and blue light has a wavelength of 486.13 nm with a weight of 1.MTF(r, s)=(1×MTF _(656.27)+2×MTF _(587.56)+1×MTF _(486.13))/(1+2+1)

Since the white-light MTF is measured only at one wavelength (840 nm),calibration may be performed for other wavelengths according to theresult of measurement, as compensation, to obtain the MTF at eachwavelength. More specifically, when the eye optical characteristicmeasuring apparatus measures eye aberration, for example, at 840 nm,color aberration W_(Δ)(X, y) corresponding to a shift from the wavefrontaberrations W₈₄₀(x, y) at a wavelength of 840 nm is measured with theuse of an eye model, W₈₄₀(x, y) is added to the color aberrationW_(Δ)(x, y), and the MTF is calculated at each wavelength from thiswavefront aberrations in the following way.W _(λ)(x, y)=W ₈₄₀(x, y)+W _(Δ)(x, y)(Contrast Sensitivity Calculation)

Next, the contrast sensitivity will be described. The contrastsensitivity is expressed by a following expression (Peter G. J. Barten,“Contrast Sensitivity of the Human Eye and Effects on Image Quality”,SPIE Optical Engineering Press 1999).

$\begin{matrix}{{S\left( {r,s} \right)} = \frac{{M_{opt}\left( {r,s} \right)}/k}{\sqrt{\frac{4}{T}\left( {\frac{1}{X_{o}^{2}} + \frac{1}{X_{\max}^{2}} + \frac{u^{2}}{N_{\max}^{2}}} \right)\left( {\frac{1}{\eta\; p\; E} + \frac{\Phi_{0}}{1 - {\mathbb{e}}^{- {({\sqrt{r^{2} + s^{2}}/u_{0}})}^{2}}}} \right)}}} & (17)\end{matrix}$Where, the respective parameters are as follows: M_(opt)(r, s): MTF ofthe eye optical system, k: S/N ratio: 3, T: weighting time of a nervoussystem: 0.1 sec, X_(o): visual angle of a matter: 3.8 deg, X_(max):maximum visual angle of space weighting: 12 deg, N_(max): maximumfrequency when weighting is performed: 15 cycles, η: quantum efficiencyof a light receptor of an eye: 0.3, p: photon conversion coefficient(ORT) of a light source: 1.24 (liquid crystal is also acceptable), E:retina illumination (Troland): 50 (cdm²)×r²π (mm)=50r²π(td) (r: pupilradius) 100 or less, φ₀: spectral density of nervous system noise: 3×108sec·deg², u₀: spatial frequency of side suppression: 7 cycles/deg. Byusing this expression, not the contrast sensitivity by the eye opticalsystem, but the contrast sensitivity of the whole optic system includingother elements (for example, nervous system) can be predicted.

FIG. 15 is an explanatory view of the contrast sensitivity. In the graphshown in FIG. 15, the vertical axis indicates the contrast sensitivitycalculated by using the foregoing expression, and the horizontal axisindicates the spatial frequency, and the graph is a one-dimensionalgraph (graph at the time of, for example, s=0) on a certain sectionpassing through the origin. By obtaining the contrast sensitivity of thewhole optic system corresponding to the spatial frequency, for example,the visibility of a stripe index can be predicted.

Besides, an eye doctor or the like can compare, for example, thecontrast sensitivity displayed on the display section with thesensitivity by subjective measurement. For example, it is possible tocompare the sensitivities of 3 cpd, 6 cpr, 9 cpd and 12 cpd in the xdirection obtained by general subjective measurement and according tovertical stripe indexes with the contrast sensitivities corresponding tothe respective spatial frequencies at the time of s=0. Incidentally,since the contrast sensitivity does not depend on the angle in the casewhere it is displayed in polar coordinates and is rotation symmetry, itcan also be displayed while the horizontal axis of the graph is made theamplitude component of the polar coordinate display.

Incidentally, the foregoing first, second, third, and fourth flowchartsand the calculation of the contrast sensitivity are combined and areused to obtain the correction values of the spherical power, theastigmatic power, and the astigmatic axis, and the visual acuity and/orthe sensitivity at the time of the correction may be measured. In thecase where the astigmatism is considered, since the spherical powercalculated by the first flowchart becomes an equivalent spherical powerS_(E), the spherical power is made S=S_(E)−(1/2)C.

6. Correction Image Simulation

6-1 First Flowchart of Correction Image Simulation

FIG. 23 is a flowchart of the correction image simulation of the stepS107.

The arithmetic part 210 calculates a best image condition (S201). Asdescribed later, the details are such that the arithmetic part 210obtains a lower order Zernike coefficient so that the Strehl ratiobecomes maximum or the phase shift becomes as small as possible, andobtains corrective correction data. As the corrective correction data,suitable data can be named among, for example, coefficientscorresponding to defocus, astigmatism components, S, C, A, higher orderspherical aberrations, higher order astigmatism aberrations, higherorder coma aberrations, the Strehl ratio and the like.

The arithmetic part 210 obtains the wavefront aberrations W(x, y) at thetime of the best image condition, and calculates the pupil function f(x,y) from W(x, y) by the following expression (S203). Detail descriptionof processes from step S205 to S211 is omitted, because each steps aresame or similar to same number of steps of FIG. 8.

The arithmetic part 210 displays the LandImage(X, Y) and PSF(X, Y) onthe display part 230 by a suitable display method of a drawing, graphicdata, a graph and/or a numerical value, and suitably stores the data inthe memory 240 (S213). The arithmetic part 210 reads out correctivecorrection data from the memory 240 as the need arises, and outputs itto the display part 230 (S215).

6-2 Calculation of Correction Data Based on Strehl Ratio

FIG. 24 shows a flowchart concerning a first example of best imagecondition calculation. FIG. 24 is the detailed flowchart concerning theforegoing step S201.

First, the arithmetic part 210 sets a threshold value for respectiveaberration quantities RMS_(i) ^(2j−I) as a branch condition (S401). Forexample, this threshold value can be made a sufficiently small value(for example, 0.1) of aberration. The arithmetic part 210 calculates theZernike coefficients C_(i) ^(2j−I) from the measured detectionwavefront, and converts them to the aberration quantities RMS_(i)^(2j−I) by the following expression (S403).

$\begin{matrix}{{RMS}_{i}^{{2j} - i} = {\sqrt{\frac{ɛ_{i}^{{2j} - i}}{2\left( {i + 1} \right)}}{C_{i}^{{2j} - i}\left( {{ɛ_{i}^{{2j} - i} = {2\mspace{14mu}\left( {{2j} = i} \right)}},{ɛ_{i}^{{2j} - i} = {1\mspace{14mu}\left( {{2j} \neq i} \right)}}} \right)}}} & (18)\end{matrix}$

The arithmetic part 210 judges whether at least one of the values ofRMS_(i) ^(2j−i) (i>2) is the threshold value or higher (S405). Here, inthe case where a judgment of No is made, it proceeds to step S419. Onthe other hand, here, when a judgment of Yes is made, the arithmeticpart 210 carries out a next processing.

That is, the arithmetic part 210 judges whether at least one of thehigher order spherical aberration quantities R₄ ⁰, R₆ ⁰ . . . ofaberration quantities RMS (R_(i) ^(2j−i)) is the threshold value orhigher (S407). Here, in the case of Yes, the arithmetic part 210 causesthe aberration to change a coefficient (C₂ ⁰) corresponding to thedefocus so that the Strehl ratio becomes maximum (S409), and on theother hand, in the case of No, it proceeds to step S411. Next, thearithmetic part 210 judges whether at least one of the asymmetricalhigher order coma aberration quantities RMS_(i) ^(2j−i) (i: odd number)is the threshold value or higher (S411). Here, in the case of Yes, thearithmetic part 210 causes the aberration to change the coefficient (C₂⁰) corresponding to the defocus so that the Strehl ratio becomes maximum(S413), and on the other hand, in the case of No, it proceeds to stepS415. Further, the arithmetic part 210 judges whether at least one ofthe higher order astigmatism aberration quantities RMS_(i) ^(2j−i) (i:even number and 2j−1≈0) is the threshold value or higher (S415). Here,in the case of Yes, the arithmetic part 210 adds astigmatism components(C₂ ⁻², C₂ ²) to the aberration so that the Strehl ratio becomes maximum(S417), and on the other hand, in the case of No, it proceeds to stepS419.

In this way, the arithmetic part 210 calculates OTF(u,

v) and PSF(X, Y) from the aberrations, and further calculates thecorrective correction data (suitable data such as coefficientscorresponding to the defocus, astigmatism components, S, C, A, higherorder spherical aberrations, higher order astigmatism aberrations,higher order coma aberrations, and Strehl ratio) from the Zernikecoefficients, and stores them in the memory 240 (S419).

Incidentally, in order to correct only a desired component among thedefocus and the astigmatism components, any of the pairs of the stepsS407 and S409, the steps S411 and S413, and the steps of S415 and S417may be omitted, or a step may be added to correct suitable higher orderaberrations or Zernike coefficients other than these. For example, inthe case where a fourth-order spherical aberration is mainly included inthe higher order aberrations, the corrective correction data can beobtained by correcting in the direction in which the defocus quantitycorresponding to the lower order aberrations are increased.

Next, the detailed processing of the steps S409, S413 and S417 will bedescribed. In the respective steps, the arithmetic part 210 carries outthe processing as follows.

In order to obtain a more suitable image plane, the arithmetic part 210adds to the wavefront aberrations W(x, y) the lower order Zernikecoefficients C_(i) ^(2j−i) (1≦i≦2) at each step presently noted for theaberration quantities comparable to the higher order aberrationquantities according to the threshold value of the last noted higherorder aberration quantities (RMS₄ ⁰, RMS₆ ⁰ . . . ) in the flow. Forexample, C₂ ⁰ is added at the step S409; C₂ ⁰, at the step 413; and C₂⁻², C₂ ², at the step S417.

Further, the pupil function f(x, y) is obtained from the wavefrontaberrations in the manner described below.f(x,y)=e ^(ikW(x,y))

(i: imaginary number, k: wave number vector (2π/λ), λ: wavelength) Thearithmetic part 210 performs the Fourier transformation on this pupilfunction f(x, y), so that an amplitude distribution U(u, v) of a pointimage is obtained as in the following expression.

$\begin{matrix}{\mspace{20mu}{{{amplitude}\mspace{20mu}{U\left( {u,v} \right)}} = {\underset{- \infty}{\overset{\infty}{\int\int}}{f\left( {x,y} \right)}\;{\exp\left\lbrack {{- \frac{\mathbb{i}}{R}}\frac{2\;\pi}{\lambda}\left( {{u\; x} + {v\; y}} \right)} \right\rbrack}\;{\mathbb{d}x}{\mathbb{d}y}}}} & (19)\end{matrix}$

-   (λ: wavelength-   R: a distance from a pupil to an image point (retina)-   (u, v): a coordinate value on a plane orthogonal to an optical axis    while an image point O is made the origin-   (x, y): a coordinate value on a pupil plane)

The arithmetic part 210 multiplies U(u, v) by its complex conjugate andobtains I(u, v) as a point image intensity distribution (PSF) by thefollowing expression.I(u,v)=U(u,v)U*(u,v)

Besides, when the center intensity of PSF at the time when there is noaberrations (W(x, y)=0) is made Io(0, 0), the Strehl ratio is defined asfollows:Strehl ratio=I(0, 0)/Io(0, 0).

In the first example, the arithmetic part 210 recursively oranalytically obtains a value of the lower order Zernike coefficientC_(ij) (1≦i≦2) so that the value of the Strehl ratio becomes maximum.

6-3 Calculation of Correction Data Based on a Phase Shift

Next, FIG. 25 is a flowchart concerning the second example of the bestimage condition calculation.

First, the arithmetic part 210 sets a threshold value for the respectiveaberration quantities RMS_(i) ^(2j−I) as a branch condition (S501). Forexample, this threshold value is made a sufficiently small value (forexample, 0.1) of aberration.

The arithmetic part 210 calculates the Zernike coefficients C_(i)^(2j−I) from the measured detection wavefront, and converts them to theaberration quantities RMS_(i) ^(2j−I) by the expression indicated in thefirst example (S503). The arithmetic part 210 judges whether at leastone of RMS_(i) ^(2j−I) (I >2) is the threshold value or higher (S505).Here, in the case of the judgment of No, it proceeds to step S519. Onthe other hand, in the case of the judgment of Yes, the arithmetic part210 carries out a next processing.

That is, the arithmetic part 210 judges whether at least one of thehigher order spherical aberration quantities R₄ ⁰, R₆ ⁰ . . . is thethreshold value or higher (S507). Here, in the case of Yes, thearithmetic part 210 causes the aberration to change the coefficient (C₂⁰) corresponding to the defocus so that the phase shift becomes as smallas possible (S509), and on the other hand, in the case of No, itproceeds to step S511. Next, the arithmetic part 210 judges whether atleast one of the higher order coma aberration quantities RMS_(i) ^(2j−I)(i: odd number) is the threshold value or higher (S511). Here, in thecase of Yes, the arithmetic part 210 causes the aberration to change thecoefficient (C₂ ⁰) corresponding to the defocus so that the phase shiftbecomes as small as possible (S513), and on the other hand, in the caseof No, it proceeds to step S515. Further, the arithmetic part 210 judgeswhether at least one of the higher order astigmatism aberrationquantities RMS_(i) ^(2j−I) (i: even number and j≈0) is the thresholdvalue or higher (S515). Here, in the case of Yes, the arithmetic part210 adds the astigmatism components (C₂ ⁻², C₂ ²) to the aberration sothat the Strehl ratio becomes maximum (S517), and on the other hand, inthe case of No, it proceeds to step S519.

In this way, the arithmetic part 210 calculates OTF(u, v) and PSF(X, Y)from the aberrations, and further calculates the corrective correctiondata (suitable data such as the coefficients corresponding to thedefocus, astigmatism components, S, C, A, higher order sphericalaberrations, higher order astigmatism aberrations, higher order comaaberrations, and Strehl ratio) from the Zernike coefficients, and storesthem in the memory 240 (S519).

Incidentally, any of the pairs of the steps S507 and S509, the stepsS511 and S513, and the steps S515 and S517 may be omitted so that only adesired component is corrected among the defocus and the astigmatismcomponents. Besides, a step may be added so that suitable higher orderaberrations or Zernike coefficients other than these is corrected.

Next, the detailed processing of the steps S509, S513 and S517 will bedescribed. The arithmetic part 210 carries out the processing asfollows.

First, as described in the detailed processing of the steps S409, S413and S417, the arithmetic part 210 obtains the point image intensitydistribution (PSF) from the expression of the wavefront at the time ofthe objective complete correction calculated from the Zernikecoefficients. Next, the arithmetic part 210 performs a Fouriertransformation (or autocorrelation) on the PSF to normalize it as in thefollowing expression and obtains OTF.

$\begin{matrix}{{{R\left( {r,s} \right)} = {\underset{- \infty}{\overset{\infty}{\int\int}}{I\left( {u,v} \right)}\;{\mathbb{e}}^{{- {\mathbb{i}}}\; 2\;\pi\;{({{r\; u} + {s\; v}})}}{\mathbb{d}u}\;{\mathbb{d}{v\left( {r,{s\text{:}\mspace{20mu} a\mspace{14mu}{variable}\mspace{14mu}{of}\mspace{14mu} a\mspace{14mu}{spatial}\mspace{14mu}{frequency}\mspace{14mu}{region}}} \right)}}}}\text{}{{OTF} = \frac{R\left( {r,s} \right)}{R\left( {0,0} \right)}}} & (20)\end{matrix}$

In general, the amplitude of a spatial frequency region and a phasedistribution R(r, s) become complex numbers, and when its real numberpart is A(r, s), and its imaginary part is B(r, s),R(r, s)=A(r, s)+iB(r, s)

and the shift of the phase (phase shift, PTF) is calculated by

$\begin{matrix}{{\phi\left( {r,s} \right)} = {\tan^{- 1}\frac{B\left( {r,s} \right)}{A\left( {r,s} \right)}}} & (21)\end{matrix}$

In the second example, the arithmetic part 210 recursively andanalytically obtains such a value of the lower order Zernike coefficientC_(i) ^(2j−I) that a value at which the R(r, s) has an extreme value isbrought to a high frequency to the extent possible, that is, the phaseshift becomes as small as possible.

Incidentally, with respect to the first example and the second exampleof the best image condition calculation, both the processings may becarried out to obtain such a condition that the Strehl ratio is large,and the phase shift is small.

7. Display Example

7.1 Display Example at the Time of Visual Acuity Measurement

FIG. 16 shows, with respect to the best image display-template matchingand as numerical data, the spherical power S, astigmatic power C, andastigmatic axis angle Ax, which are compensation correction data, thepupil diameter, and the spherical power S, astigmatic power C,astigmatic axis angle Ax, and corrected visual acuity, which aremeasured values before the compensation correction. Further, correctedvisual acuity in the correction data may be displayed. In this example,since the component of the higher order aberration has a predeterminedvalue or more, a difference in numerical value occurs between thecompensation correction data and the measured values. In these drawings,the wavefront aberration, PSF, OTF, OTF (two-dimensional display), S, C,Ax, Landolt's ring, visibility of the index and the like are displayedon the display section 230. Further, for example, the contrastsensitivity shown in FIG. 15 may be displayed on the display section230. Besides, some of them may be suitably selected and displayed.

FIG. 17 is a view showing a display example concerning the comparisonbetween pre-compensation and post-compensation. This drawing shows thecorrected visual acuity, wavefront aberration, and visibility of theLandolt's ring, which are obtained before and after the compensation,and the pupil diameter. As shown in the drawing, it is indicated thatafter the compensation correction, the wavefront aberration becomesrelatively uniform, and the Landolt's ring is relatively well seen.Besides, the corrected visual acuity of the subjective eye under anenvironment after the compensation correction is shown.

FIG. 18 is an explanatory view of an example of prescription data foreyeglasses/contacts. FIG. 19 is an explanatory view of an example ofdata for refractive surgery.

The respective data are stored in the memory 240 from the calculationsection 210, and/or displayed on the display section 230. This exampleindicates that in the data of the case where the refractive surgery isperformed while only the SCA is made the compensation correction data,the corrected visual acuity is improved by performing the correction insuch a way that the value of S in the compensation correction data isintensified, the value of C is weakened, and the axial direction of A isslightly changed. Besides, FIG. 19 shows expected values of therespective parameters under the illustrated pupil diameter after thecompensation correction.

FIG. 20 is an explanatory view of an example of prescription data foreyeglasses/contacts when the environmental condition is changed. Forexample, the pupil diameter of the eye 60 to be measured is measured inthe illumination states corresponding to the respective environmentalconditions, and the correction data and corrected visual acuities at therespective pupil diameters are displayed. It is indicated that thecompensation correction data slightly varies according to the pupildiameter. That is, it is indicated that the optimum prescription valuevaries according to the environment of the subjective eye. Besides, forexample, the doctor considers the environment of the subjective eye, andcan select the prescription value. Incidentally, the environmentalconditions to be displayed can be suitably changed.

In the example shown in FIG. 20, although the correction datacorresponding to the respective environmental conditions are obtained,and the visual acuities under the environmental conditions aredisplayed, the visual acuity under another environmental condition canalso be estimated and displayed. For example, in the case wherecorrection is made by the compensation correction data in the daytime,the visual acuities in the daytime, under a fluorescent lamp and in aroom and daytime can also be predicted and displayed.

FIG. 21 is an explanatory view of an example of pupil data when theenvironmental condition is changed. For example, the pupil diameter ofthe eye 60 to be measured is measured under illumination statescorresponding to the respective environmental conditions, and the shiftamount (x direction, y direction) from the limbus center of the pupilcenter at the respective pupil diameters and the corrected visual acuityare shown. It is indicated that the pupil center is shifted by thechange of the environmental condition, and the center (origin) at thetime of analysis is shifted.

FIG. 22 is a comparison view of prescription data foreyeglasses/contacts and measurement at constant pupil diameters. Thereare shown, for example, the correction data and corrected visualacuities in the case where similarly to the conventional measurement,the pupil diameter is made 4 mm and 6 mm and the case where the pupildiameter is measured (for example, under illumination of 50 1×). Thecorrection data and corrected visual acuity slightly vary between thecase where the pupil diameter is fixed and the case where it ismeasured. Incidentally, although FIG. 21 shows, as an example, datausing the pupil diameter under the illuminated of 50 1×, it is possibleto estimate the visual acuity of the subjective eye under an appropriateenvironment by suitably changing the illumination condition.

Incidentally, in the foregoing drawing, although the visual acuity isexpressed by the decimal visual acuity, it may be displayed by thelogMAR visual acuity. Besides, the condition to be displayed can besuitably changed.

7.2 Display Example in Correction Data Simulation

FIG. 26 shows, with respect to the best image display-Strehloptimization and as numerical data, the spherical power S, astigmaticpower C, and astigmatic axis angle Ax, which are compensation correctiondata, the spherical power S, astigmatic power C, and astigmatic axisangle Ax, which are measured values before the compensation correction,and the pupil diameter used for the calculation of the correction data.In this example, since the components of the higher order aberrationshave predetermined values or more, a difference in numerical valueoccurs between the compensation correction data and the measured values.

FIG. 27 shows, with respect to the best image display-PTF optimizationand as numerical data, the spherical power S, astigmatic power C, andastigmatic axis angle Ax, which are compensation correction data, thespherical power S, astigmatic power C, and astigmatic axis angle Ax,which are measured values before the compensation correction, and thepupil diameter used for the calculation of the correction data. In thisexample, since the components of the higher order aberrations havepredetermined values or more, a difference in numerical value occursbetween the compensation correction data and the measured values.

FIG. 28 is a view showing a display example concerning the comparisonbetween pre-compensation and post-compensation. This drawing shows thewavefront aberrations before and after the compensation, thevisibilities of the Landolt's ring, Strehl ratios, and the pupildiameter. As shown in the drawing, the Strehl ratio after thecompensation is higher, the wavefront aberrations become relativelyuniform, and the Landolt's ring can also be relatively well seen.

FIG. 29 is an explanatory view of an example of prescription data foreyeglasses/contacts. FIG. 30 is an explanatory view of an example ofdata for refractive surgery.

The respective data are stored from the calculation section 210 into thememory 240, and/or are displayed on the display section 230. Thisexample indicates that in the data of the case where the refractivesurgery is performed while only the SCA are made the compensationcorrection data, the Strehl ratio becomes high and the correction effectbecomes high by performing the correction in such a manner that thevalue of S in the compensation correction data is intensified, the valueof C is weakened, and the axial direction of A is slightly changed.

FIG. 31 is an explanatory view of an example of prescription data foreyeglasses/contacts when the environmental condition is changed. Forexample, the pupil diameters of the eye 60 to be measured are measuredunder illumination states corresponding to the respective environmentalconditions, and the correction data at the respective pupil diametersare displayed. It is indicated that the compensation correction dataslightly varies according to the pupil diameters. That is, it isindicated that the optimum prescription value varies according to theenvironment of the subjective eye. Besides, for example, the doctor orthe like considers the environment of the subjective eye, and can selectthe prescription value. Incidentally, the environmental condition to bedisplayed can be suitably changed.

FIG. 32 is a comparison view of prescription data foreyeglasses/contacts and measurement at constant pupil diameters. Forexample, correction data when the pupil diameter is made 4 mm and 6 mmsimilarly to the conventional measurement, and correction data of thecase where the pupil diameter is measured (for example, underillumination of 50 1×) are displayed. The correction data slightlyvaries between the case where the pupil diameter is fixed and the casewhere it is measured. In this embodiment, it is possible to obtain theoptimum correction data corresponding to the pupil diameter of thesubjective eye. Incidentally, the condition to be displayed can besuitably changed.

8. Modified Example

A modified example of the invention will be described below.

This modified example modifies the calculation method of the best imagecondition at S201 of FIG. 23.

A component of an i-th row and a j-th column of Jacobian matrix A is

$\begin{matrix}{A_{ij} = \frac{\partial{f_{i}(x)}}{\partial x_{j}}} & (22)\end{matrix}$

Where, f_(i)(x) is the Strehl ratio, the PTF corresponding to a suitablefrequency, or some values of the PTF corresponding to pluralfrequencies. Besides, it may be a combination of the Strehl ratio andthe PTF. Besides, a vector x is an adjustable parameter, and here, thesphere (or defocus corresponding to that) and two astigmatismscorrespond to that.

The calculation expressions of the Strehl ratio and the PTF are alreadygiven. The ideal value of the Strehl ratio is 1. It is assumed that thefollowing expression expresses the Strehl ratio.f ₁(x)=fs(hc, c ₂ ⁰ , c ₂ ⁻² , c ₂ ²)  (23)

Where, f₁ denotes the expression of the same indication in theexpression (22).

Besides, for example, as the PTF, values corresponding to the spatialfrequency of 3 cpd, 6 cpd, 12 cpd, and 18 cpd are taken, and it is idealthat this is 0.f ₂(x)=f _(PTF3)(hc, c ₂ ⁰ , c ₂ ⁻² , c ₂ ²)  (24)f ₃(x)=f _(PTF6)(hc, c ₂ ⁰ , c ₂ ⁻² , c ₂ ²)  (25)f ₄(x)=f _(PTF12)(hc, c ₂ ⁰ , c ₂ ⁻² , c ₂ ²)  (26)f ₅(x)=f _(PTF18)(hc, c ₂ ⁰ , c ₂ ⁻² , c ₂ ²)  (27)

In the expressions (23), (24), (25), (26) and (27), hc denotes a vectorof higher order aberration coefficients, c₂ ⁰ denotes a coefficient of adefocus term relating to the sphere, c₂ ⁻² and c₂ ² denote coefficientsof terms relating to astigmatism. The vector hc is given by wavefrontaberration measurement, and here, it is constant. Thus, the remainingthree coefficients are made a parameter vector x and are suitably movedto guide f_(s) to the minimum value, which is a task here.

Here, the partial differentiation of the expression (22) can becalculated by slightly moving the parameters to prepare a change table,and the Jacobian matrix in this system is obtained.

Now, when the task here is expressed in other words again, sincenonlinear optimization in the case where the Jacobian, that is, thepartial differential coefficient is known has only to be performed, whenoptimizing algorism of a Newton method system is used, it is easy toobtain a solution since the example is simple. When a specific solutionaccording to a corrected Marquardt method is stated, a correction vectorΔx can be obtained by(A ^(t) WA+λI)Δx=A ^(t) W(y−f(x))  (28)

Here, t at the shoulder of the matrix denotes a transposed matrix, and Wdenotes a weighting matrix. The first element of y corresponds to Strehlratio, and the remainder corresponds to four components of PTF, it hasonly to be made (1,0,0,0,0)^(t). λ is called a damping factor, and it ismade large at first, and then, it is made small in accordance with goingof optimization.

$\begin{matrix}{W = \begin{pmatrix}w_{1} & 0 & 0 & 0 & 0 \\0 & w_{2} & 0 & 0 & 0 \\0 & 0 & w_{3} & 0 & 0 \\0 & 0 & 0 & w_{4} & 0 \\0 & 0 & 0 & 0 & w_{5}\end{pmatrix}} & (29)\end{matrix}$

A subscript corresponds to a subscript of f. Weighting suitable for theobject of a prescription can be freely performed, for example, when theStrehl ratio is desired to be selectively optimized, w₁ is made large.The expression (7) is applied several times, and whenS=W(y−f(x))  (30)

becomes suitably small (when a conversion condition is satisfied), thecalculation is stopped, and x at that time is made the solution. Bythis, the optimum the sphere (or defocus corresponding to that) and twoastigmatisms are obtained.

Incidentally, the best image condition calculation can also be performedby finding out the position where the Strehl ratio becomes maximum orthe phase shift (PTF) becomes substantially zero while the defocusamount and/or the astigmatism component is changed slightly. Besides, aposition where the Strehl ratio becomes maximum or the phase shift (PTF)becomes substantially zero may be obtained by using a well-known Newtonmethod.

9. Appendix

The apparatus and system of the ophthalmic data measurement according tothe invention can be provided through an ophthalmic data measurementprogram for causing a computer to execute the respective procedures, acomputer readable recording medium on which the ophthalmic datameasurement program is recorded, a program product including theophthalmic data measurement program and loadable into the internalmemory of a computer, a computer, such as a server, including theprogram, or the like.

Besides, although the measurement data indicating the refractive powerdistribution of the eye to be measured is obtained by the optical system100 shown in FIG. 1, no limitation is made to this, and the structurecan be made by another aberrometer or the like.

INDUSTRIAL APPLICABILITY

According to the invention, the optical characteristic corresponding tothe pupil diameter of the eye to be examined and the correction dataclose to the optimum prescription value are calculated, and moreaccurate measurement can be performed.

Besides, according to the invention, in the results of measurement bythe eye characteristic measuring apparatus which can measure higherorder aberrations, in the case where the higher order aberrations areincluded, the lower order aberrations corresponding to the time of theobjective complete correction are not made the compensation correctiondata, and for example, the optical performance is evaluated by theStrehl ratio or the phase shift, the lower order aberration amount toincrease the Strehl ratio and/or to reduce the phase shift iscalculated, and the compensation correction data, such as S, C, A, atthat time are obtained, so that the correction data close to the optimumprescription value of eyeglasses/contacts can be obtained. Further, thesimulation of the visibility of the index for eye examination isperformed, and the appropriate correction element is obtained, so thatit is also possible to obtain the correction data close to thesubjective value.

According to the invention, the visual acuity of the eye to be examinedcan be estimated under the brightness (for example, in the daytime or ina room) corresponding to the environment of the subjective eye in dailylife. Besides, according to the invention, in view of the pupil diameterof the eye to be examined in daily life, the visual acuity with respectto the index of high contrast and/or low contrast can be estimated.According to the invention, the contrast sensitivity in view of thepupil diameter can be predicted. Further, according to the invention, byusing the pupil diameter under the brightness (for example, in thedaytime or in a room) corresponding to the environment of the subjectiveeye, the correction data close to the optimum prescription value underthe environment is obtained, and the visual acuity under the environmentof the subjective eye can be estimated by the correction using theobtained correction data. Besides, the simulation of an index such asthe Landolt's ring on the retina in view of the size of the pupil areacalculated in the halfway process is also singly effective.

1. An ophthalmic data measuring apparatus comprising: a first lightsource part to emit a light flux of a first wavelength; a firstilluminating optical system for performing illumination to condense thelight flux from the first light source part on a vicinity of a retina ofan eye to be examined; a first light receiving optical system forreceiving a part of the light flux reflected by and returning from theretina of the eye to be examined through a first conversion member toconvert it into at least substantially 17 beams; a first light receivingpart for receiving the received light flux of the first light receivingoptical system; and a calculation section to perform Zernike analysisbased on an inclination angle of the light flux obtained by the firstlight receiving part, to obtain an optical characteristic of the eye tobe examined, and (1) to estimate one of or two or more of a visualacuity, the optical characteristic and a sensitivity of the eye to beexamined under an observation condition corresponding to an environmentof the eye to be examined, or (2) to calculate appropriate correctiondata suitable for the eye to be examined, wherein the calculationsection comprises: first means for obtaining measurement data indicatinga refractive power distribution of the eye to be examined and pupil dataincluding a value of a pupil diameter of the eye to be examined or apupil diameter image and for obtaining lower order aberrations andhigher order aberrations based on an observation condition parameterincluding the measurement data and the pupil data; second means forcalculating an evaluation parameter indicating quality of visibility bythe eye to be examined based on the observation condition parameterand/or the obtained lower order aberrations and the higher orderaberrations; and third means for, in accordance with the calculatedevaluation parameter, (1) estimating one of or two or more of the visualacuity, the optical characteristic and the sensitivity, of the eye to beexamined under the observation condition corresponding to theenvironment of a subjective eye or (2) calculating the appropriatecorrection data suitable for the eye to be examined by changing thelower order aberration.
 2. The ophthalmic data measuring apparatusaccording to claim 1, wherein the pupil data is data corresponding tothe observation condition in accordance with the environment of thesubjective eye and/or the second means simulates the visibility of animage by the eye to be examined and calculates the evaluation parameterindicating the quality of the visibility.
 3. The ophthalmic datameasuring apparatus according to claim 1, wherein the first means isconstructed to cause the calculation section to receive the measurementdata indicating the refractive power distribution of the eye to beexamined, and the pupil data including the pupil image at a time ofmeasurement or under a correction environment in which the correctiondata is obtained, to calculate a pupil diameter under the observationcondition or the correction environment based on the received pupildata, and to obtain the lower order aberrations and the higher orderaberrations based on the received measurement data and the calculatedpupil diameter.
 4. The ophthalmic data measuring apparatus according toclaim 1, wherein the first means comprises: means by which thecalculation section receives the measurement data indicating therefractive power distribution of the eye to be examined and the pupildata including the pupil image at the time of measurement or under thecorrection environment; means by which the calculation section detectspoints on a pupil edge based on the received pupil data; means by whichthe calculation section calculates a focal point and a major axis and/ora minor axis of an ellipse fitted to the detected points; means by whichthe calculation section calculates the pupil diameter of the eye to beexamined based on the major axis and/or the minor axis of the ellipse;and means by which the calculation section obtains the lower orderaberrations and the higher order aberrations based on the receivedmeasurement data and the calculated pupil diameter.
 5. The ophthalmicdata measuring apparatus according to claim 1, further comprising: asecond light source to emit a light flux of a second wavelength; asecond illuminating optical system to illuminate a vicinity of a corneaof the eye to be examined with a predetermined pattern and by the secondillumination light flux from the second light source; a second lightreceiving optical system to receive the second illumination light fluxreflected by and returning from the vicinity of the cornea of the eye tobe examined; a second light receiving part to receive the received lightflux of the second light receiving optical system; and a pupil dataformation part to form pupil data of the eye to be examined from outputof the second light receiving part, wherein the calculation section isconstructed to obtain the pupil data by the pupil data formationsection.
 6. The ophthalmic data measuring apparatus according to claim1, further comprising an anterior ocular segment illuminating partconstructed to be capable of illuminating an anterior ocular segment ofthe eye to be examined at desired brightness, wherein the calculationsection is constructed to adjust the anterior ocular segmentilluminating part to produce brightness corresponding to a predeterminedobservation condition or correction environment, and to estimate thevisual acuity of the eye to be examined and/or the sensitivity based onan output signal of the first light receiving part in the illuminationstate and the pupil data, or to obtain the appropriate correction datasuitable for the eye to be examined.
 7. The ophthalmic data measuringapparatus according to claim 6, wherein the anterior ocular segmentilluminating part is constructed to perform measurement by sequentiallychanging the illumination state from a dark one to a bright one in acase where plural illumination states are formed.
 8. The ophthalmic datameasuring apparatus according to claim 1, wherein the second meanscomprises: means by which the calculation section simulates thevisibility of an index for eye examination by the eye to be examinedbefore or after correction to form index image data; means by which thecalculation section compares the index image data with pattern data ofthe index for eye examination by patterning matching; and means by whichthe calculation section calculates the evaluation parameter based on acomparison result by the pattern matching.
 9. The ophthalmic datameasuring apparatus according to claim 1, wherein the calculationsection is constructed to estimate a high contrast visual acuity and/ora low contrast visual acuity of the eye to be examined by using a highcontrast index for eye examination and/or a low contrast index for eyeexamination.
 10. The ophthalmic data measuring apparatus according toclaim 1, wherein with respect to the third means, the calculationsection judges whether the evaluation parameter indicating visibility ofan index for eye examination satisfies a previously specified reference,and estimates the visual acuity in accordance with a size of the indexfor eye examination corresponding to the evaluation parameter satisfyingthe reference.
 11. The ophthalmic data measuring apparatus according toclaim 10, wherein the calculation section further comprises: means forobtaining data of an MTF (Modulation Transfer Function) indicating atransfer characteristic of the eye to be examined based on the lowerorder aberrations and the higher order aberrations; and means forestimating a contrast sensitivity based on the obtained data of the MTF.12. The ophthalmic data measuring apparatus according to claim 1,wherein with respect to the second means, the calculation sectionobtains data of an MTF (Modulation Transfer Function) indicating atransfer characteristic of the eye to be examined based on the lowerorder aberrations and the higher order aberrations; and with respect tothe third means, the calculation section estimates a contrastsensitivity based on the obtained data of the MTF.
 13. The ophthalmicdata measuring apparatus according to claim 1, wherein the calculationsection further comprises means for obtaining a pupil center positionunder the observation condition based on the received pupil data and forcalculating a shift amount of the pupil center position to shift ananalysis center.
 14. The ophthalmic data measuring apparatus accordingto claim 1, wherein the calculation section further comprises means forstoring one of or two or more of the visual acuity, the sensitivity, thecorrection data, and a simulation result into a memory or displayingthem on a display section.
 15. The ophthalmic data measuring apparatusaccording to claim 1, wherein the third means is constructed toestimate, as the optical characteristic, an MTF (Modulation TransferFunction) of the eye to be examined, and a point spread function (PSF).16. The ophthalmic data measuring apparatus according to claim 1,wherein the calculation section further comprises means for obtainingthe appropriate correction data suitable for the eye to be examined bychanging the lower order aberration corresponding to defocus inaccordance with the evaluation parameter calculated by the second meansand for simulating the visibility of an image by the eye to be examinedat a time of correction based on the correction data to furthercalculate an evaluation parameter, and estimates the visual acuityand/or the sensitivity at the time of correction.
 17. The ophthalmicdata measuring apparatus according to claim 1, wherein the calculationsection further comprises means for obtaining appropriate correctiondata suitable for the eye to be examined by changing the lower orderaberration corresponding to an astigmatic component in accordance withthe evaluation parameter calculated by the second means and forsimulating the visibility of an image by the eye to be examined at atime of correction based on the correction data to further calculate anevaluation parameter, and estimates the visual acuity and/or thesensitivity at the time of correction.
 18. The ophthalmic data measuringapparatus according to claim 1, wherein the calculation section furthercomprises fourth means for simulating a Landolt's ring based on thecalculated correction data or a luminance distribution image of anarbitrary image, and storing the correction data and/or a simulationresult into a memory or displaying it on a display section.
 19. Theophthalmic data measuring apparatus according to claim 1, wherein withrespect to the third means, in a case where a higher order sphericalaberration or an unsymmetrical higher order coma aberration has apredetermined value or more, the calculation section changes the lowerorder aberration corresponding to defocus based on the evaluationparameter and obtains the appropriate correction data suitable for theeye to be examined.
 20. The ophthalmic data measuring apparatusaccording to claim 1, wherein with respect to the third means, in a casewhere a higher order astigmatic aberration has a predetermined value ormore, the calculation section changes the lower order aberrationcorresponding to an astigmatic component based on the evaluationparameter and obtains the appropriate correction data suitable for theeye to be examined.
 21. The ophthalmic data measuring apparatusaccording to claim 1, wherein with respect to the second means, thecalculation section calculates a Strehl ratio as the evaluationparameter based on the obtained lower order aberrations and the higherorder aberrations, and with respect to the third means, the calculationsection changes a predetermined lower order aberration to increase theStrehl ratio and calculates the appropriate correction data suitable forthe eye to be examined.
 22. The ophthalmic data measuring apparatusaccording to claim 1, wherein with respect to the second means, thecalculation section calculates a phase shift as the evaluation parameterbased on the obtained lower order aberrations and the higher orderaberrations, and with respect to the third means, the calculationsection changes the lower order aberration to decrease a phase shift andcalculates the appropriate correction data suitable for the eye to beexamined.
 23. The ophthalmic data measuring apparatus according to claim1, wherein the second means comprises: means by which the calculationsection forms data of an MTF (Modulation Transfer Function) indicating atransfer characteristic of the eye to be examined after correction basedon the lower order aberrations and the higher order aberrations, andmeans by which the calculation section calculates the evaluationparameter based on the formed data of the MTF.
 24. The ophthalmic datameasuring apparatus according to claim 1, wherein with respect to thesecond means, the calculation section forms, as the evaluationparameter, a relational expression between a Strehl ratio and a phaseshift based on the lower order aberrations and the higher orderaberrations, and with respect to the third means, the calculationsection changes the lower order aberration to obtain a condition underwhich the Strehl ratio becomes maximum and the phase shift becomessubstantially zero, and makes the lower order aberration at that timethe appropriate correction data.
 25. An ophthalmic data measurementprogram for causing a computer to execute: a first step at which acalculation section obtains measurement data indicating a refractivepower distribution of an eye to be examined and pupil data including avalue of a pupil diameter of the eye to be examined or a pupil diameterimage, and obtains lower order aberrations and higher order aberrationsbased on an observation condition parameter including the measurementdata and the pupil data; a second step at which the calculation sectioncalculates an evaluation parameter indicating quality of visibility bythe eye to be examined based on the observation condition parameterand/or the obtain lower order aberrations and the higher orderaberrations; and a third step at which in accordance with the calculatedevaluation parameter, the calculation section estimates one of or two ormore of a visual acuity, an optical characteristic and a sensitivity ofthe eye to be examined under an observation condition corresponding toan environment of a subjective eye, or calculates appropriate correctiondata suitable for the eye to be examined by changing the lower orderaberration.
 26. An ophthalmic data measurement program for causing acomputer to execute: a first step at which a calculation sectionreceives measurement data indicating a refractive power distribution ofan eye to be examined, and obtains lower order aberrations and higherorder aberrations based on the measurement data; a second step at whichthe calculation section calculates an evaluation parameter indicatingquality of visibility by the eye to be examined based on the obtainedlower order aberrations and the higher order aberrations; and a thirdstep at which the calculation section calculates appropriate correctiondata suitable for the eye to be examined by changing the lower orderaberration in accordance with the calculated evaluation parameter. 27.An eye characteristic measuring apparatus comprising: a first lightsource part to emit a light flux of a first wavelength; a firstilluminating optical system for performing illumination to condense thelight flux from the first light source part on a vicinity of a retina ofan eye to be examined; a first light receiving optical system forreceiving a part of the light flux reflected by and returning from theretina of the eye to be examined through a first conversion member toconvert it into at least substantially 17 beams; a first light receivingpart for receiving the received light flux of the first light receivingoptical system; and a calculation section for receiving pupil dataincluding a pupil image of the eye to be examined in a measurementenvironment, calculating a pupil diameter under the measurementenvironment based on the received pupil data, and obtaining an opticalcharacteristic of the eye to be examined based on the calculated pupildiameter and an output signal from the first light receiving part.